Wikipedia:WikiProject Mathematics/PlanetMath Exchange/46-XX Functional analysis: Difference between revisions

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Line 3: ==46-00 General reference works (handbooks, dictionaries, bibliographies, etc.)== * PM: [http://planetmath.org/?op=getobj&from=objects&id=4434 T_f is a distribution of zeroth order], id=4434 -- WP: [[Distribution]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=4434 T_f is a distribution of zeroth order], id=4434 -- WP: [[Distribution (mathematics)\|Distribution]] -- Status: ::PM article is a proof which is not included in WP; WP doesn't even define the ''order'' of a distribution. [[User:Jitse Niesen\|Jitse Niesen]] 13:32, 31 Jan 2005 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=4473 \operatorname{p.\!v.}(\frac{1}{x}) is a distribution of first order], id=4473 -- WP: [[Distribution (mathematics)\|distribution]] -- Status: ::PM article is a proof which is not included in WP; p.v. (1/x) is a nice example of a distribution which should be mentioned in WP. Connection with [[renormalization]]? [[User:Jitse Niesen\|Jitse Niesen]] 13:32, 31 Jan 2005 (UTC) Line 19 ⟶ 20: :::I recently split the page from [[bounded set]] and added the theorem from PM. [[User:MathMartin\|MathMartin]] 11:49, 4 May 2005 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=4472 Cauchy principal part integral], id=4472 -- WP ~~guess~~: [[Cauchy principal ~~part integral~~value]] -- Status: '''M''' : Copied the most essential part, as to not disturb too much the existing article. [[User:Oleg Alexandrov\|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov\|talk]]) 04:52, 10 March 2006 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=6195 Cauchy sequence], id=6195 -- WP: [[Cauchy sequence]] -- Status: '''A''' ::Our artilcle is more complete. [[User:Paul August\|Paul August ]] [[User_talk:Paul August\|☎]] 15:03, Jan 31, 2005 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=4570 cone], id=4570 -- WP guess: [[cone]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=4468 delta distribution], id=4468 -- WP guess: [[delta distribution]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=4427 distribution], id=4427 -- WP guess: [[Distribution (mathematics)\|distribution]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=4433 every locally integrable function is a distribution], id=4433 -- WP guess: [[every locally integrable function is a distribution]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=5556 function spaces], id=5556 -- WP guess: [[function spaces]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=4477 localization for distributions], id=4477 -- WP guess: [[localization for distributions]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=4424 locally convex topological vector space], id=4424 -- WP guess: [[locally convex topological vector space]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=4440 operations on distributions], id=4440 -- WP guess: [[operations on distributions]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=4437 proof of convergence theorem], id=4437 -- WP guess: [[proof of convergence theorem]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=4525 sequential characterization of boundedness], id=4525 -- WP guess: [[sequential characterization of boundedness]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=4568 smooth distribution], id=4568 -- WP guess: [[smooth distribution]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=4484 support of distribution], id=4484 -- WP guess: [[support of distribution]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=4528 symmetric set], id=4528 -- WP guess: [[symmetric set]] -- Status: '''C''' :[[User:TakuyaMurata\|Taku]] ([[User talk:TakuyaMurata\|talk]]) 00:38, 3 April 2009 (UTC) PM: [http://planetmath.org/?op=getobj&from=objects&id=7453 balanced set], id=7453 -- WP guess: [[balanced set]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7459 boundedness in a topological vector space generalizes boundedness in a metric space], id=7459 -- WP guess: [[boundedness in a topological vector space generalizes boundedness in a metric space]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7447 cone], id=7447 -- WP guess: [[cone]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=6723 weak convergence], id=6723 -- WP guess: [[weak convergence]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=8219 Hilbert basis], id=8219<sup style="color:red">new!</sup> -- WP guess: [[Hilbert basis]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=9771 invariant subspace problem], id=9771<sup style="color:red">new!</sup> -- WP guess: [[invariant subspace problem]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=8208 modular mappings in vector spaces over the field of complex numbers], id=8208<sup style="color:red">new!</sup> -- WP guess: [[modular mappings in vector spaces over the field of complex numbers]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=8374 modular space], id=8374<sup style="color:red">new!</sup> -- WP guess: [[modular space]] -- Status: ==46A03 General theory of locally convex spaces== * PM: [http://planetmath.org/?op=getobj&from=objects&id=5921 Krein-Milman theorem], id=5921 -- WP: [[Krein-Milman theorem]] -- Status: '''C''' :: [[User:Oleg Alexandrov\|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov\|talk]]) 19:16, 20 November 2005 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=7251 proof of Krein-Milman theorem], id=7251 -- WP guess: [[proof of Krein-Milman theorem]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=6855 weak-* topology], id=6855 -- WP guess: [[weak-* topology]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=9703 anti-cone], id=9703<sup style="color:red">new!</sup> -- WP guess: [[anti-cone]] -- Status: ==46A08 Barrelled spaces, bornological spaces== * PM: [http://planetmath.org/?op=getobj&from=objects&id=8902 barrel], id=8902<sup style="color:red">new!</sup> -- WP guess: [[barrel]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=8003 bornological space], id=8003<sup style="color:red">new!</sup> -- WP guess: [[bornological space]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=8004 bounded set], id=8004<sup style="color:red">new!</sup> -- WP guess: [[bounded set]] -- Status: ==46A20 Duality theory== * PM: [http://planetmath.org/?op=getobj&from=objects&id=9667 hyperplane separation], id=9667<sup style="color:red">new!</sup> -- WP guess: [[hyperplane separation]] -- Status: ==46A30 Open mapping and closed graph theorems; completeness (including $B$-, $B r$-completeness)== * PM: [http://planetmath.org/?op=getobj&from=objects&id=3702 closed graph theorem], id=3702 -- WP: [[closed graph theorem]] -- Status: '''A''' :: [[User:Oleg Alexandrov\|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov\|talk]]) 19:01, 20 November 2005 (UTC) Line 63 ⟶ 103: * PM: [http://planetmath.org/?op=getobj&from=objects&id=6472 proof of closed graph theorem], id=6472 -- WP: [[proof of closed graph theorem]] -- Status: '''N''' :: [[User:Oleg Alexandrov\|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov\|talk]]) 19:01, 20 November 2005 (UTC) ==46A40 Ordered topological linear spaces, vector lattices== ==46A55 Convex sets in topological linear spaces; Choquet theory== * PM: [http://planetmath.org/?op=getobj&from=objects&id=4443 convex hull of S is open if S is open], id=4443 -- WP guess: [[convex hull of S is open if S is open]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=~~5587 proof that the~~4443 convex hull of S is open if S is open], id=~~5587~~4443 -- WP guess: [[~~proof that the~~ convex hull of S is open if S is open]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=5587 proof that the convex hull of S is open if S is open], id=5587 -- WP guess: [[proof that the convex hull of S is open if S is open]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7137 conical neighborhood], id=7137 -- WP guess: [[conical neighborhood]] -- Status: ==46A99 Miscellaneous== * PM: [http://planetmath.org/?op=getobj&from=objects&id=3066 Heine-Cantor theorem], id=3066 -- WP: [[Heine-Cantor theorem]] -- Status: '''M''' ::[[User:AdamSmithee\|AdamSmithee]] 15:29, 3 February 2006 (UTC) Line 77 ⟶ 123: * PM: [http://planetmath.org/?op=getobj&from=objects&id=1744 topological vector space], id=1744 -- WP guess: [[topological vector space]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=6911 proof of Heine-Cantor theorem], id=6911 -- WP guess: [[proof of Heine-Cantor theorem]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=9857 Riesz representation theorem (of linear functionals on function spaces)], id=9857<sup style="color:red">new!</sup> -- WP guess: [[Riesz representation theorem (of linear functionals on function spaces)]] -- Status: ==46Axx Topological linear spaces and related structures== ==46B03 Isomorphic theory (including renorming) of Banach spaces== * PM: [http://planetmath.org/?op=getobj&from=objects&id=4315 hyperbolic isomorphism], id=4315 -- WP guess: [[hyperbolic isomorphism]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=4315 hyperbolic isomorphism], id=4315 -- WP guess: [[hyperbolic isomorphism]] -- Status: ==46B04 Isometric theory of Banach spaces== * PM: [http://planetmath.org/?op=getobj&from=objects&id=8524 Mazur-Ulam theorem], id=8524<sup style="color:red">new!</sup> -- WP guess: [[Mazur-Ulam theorem]] -- Status: ==46B07 Local theory of Banach spaces== * PM: [http://planetmath.org/?op=getobj&from=objects&id=5927 Lipschitz inverse mapping theorem], id=5927 -- WP guess: [[Lipschitz inverse mapping theorem]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=5927 Lipschitz inverse mapping theorem], id=5927 -- WP guess: [[Lipschitz inverse mapping theorem]] -- Status: ==46B10 Duality and reflexivity== * PM: [http://planetmath.org/?op=getobj&from=objects&id=6471 Banach-Alaoglu theorem], id=6471 -- WP: [[Banach-Alaoglu theorem]] -- Status: '''A''' ::[[User:AdamSmithee\|AdamSmithee]] 15:38, 3 February 2006 (UTC) Line 90 ⟶ 149: * PM: [http://planetmath.org/?op=getobj&from=objects&id=5229 weak* convergence in normed linear space], id=5229 -- WP guess: [[weak* convergence in normed linear space]] -- Status: '''NC''' ::[[User:AdamSmithee\|AdamSmithee]] 15:38, 3 February 2006 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=6917 Proof of Banach-Alaoglu theorem], id=6917 -- WP guess: [[Proof of Banach-Alaoglu theorem]] -- Status: ==46B15 Summability and bases== ==46B20 Geometry and structure of normed linear spaces== * PM: [http://planetmath.org/?op=getobj&from=objects&id=5399 \lim_{p \to \infty} \lVert x \rVert_p = \lVert x \rVert_{\infty}], id=5399 -- WP guess: [[\lim_p \to \infty \lVert x \rVert_p = \lVert x \rVert_\infty]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=~~6611~~5399 ~~Banach-Mazur~~\lim_{p \to \infty} \lVert x \rVert_p = \lVert x ~~compactum~~\rVert_{\infty}], id=~~6611~~5399 -- WP guess: [[~~Banach-Mazur~~\lim_p ~~compactum~~\to \infty \lVert x \rVert_p = \lVert x \rVert_\infty]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=6611 Banach-Mazur compactum], id=6611 -- WP guess: [[Banach-Mazur compactum]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=6240 basic properties of seminorms], id=6240 -- WP guess: [[basic properties of seminorms]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=3252 Hahn-Banach theorem], id=3252 -- WP guess: [[Hahn-Banach theorem]] -- Status: Status: '''A''' :: [[User:Oleg Alexandrov\|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov\|talk]]) 22:58, 10 December 2005 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=6515 Minkowski's function], id=6515 -- WP guess: [[Minkowski's function]] -- Status: '''A''' :: [[User:Oleg Alexandrov\|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov\|talk]]) 05:03, 10 March 2006 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=4127 proof of Hahn-Banach theorem], id=4127 -- WP guess: [[proof of Hahn-Banach theorem]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=2322 seminorm], id=2322 -- WP guess: [[seminorm]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=91 vector norm], id=91 -- WP guess: [[vector norm]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=6967 sub-linear], id=6967 -- WP guess: [[sub-linear]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=9087 Golab's theorem], id=9087<sup style="color:red">new!</sup> -- WP guess: [[Golab's theorem]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=9086 normed plane], id=9086<sup style="color:red">new!</sup> -- WP guess: [[normed plane]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=8823 nuclear space], id=8823<sup style="color:red">new!</sup> -- WP guess: [[nuclear space]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7704 properties of Minkowski's functional], id=7704<sup style="color:red">new!</sup> -- WP guess: [[properties of Minkowski's functional]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=92 vector p-norm], id=92<sup style="color:red">new!</sup> -- WP guess: [[vector p-norm]] -- Status: ==46B25 Classical Banach spaces in the general theory== * PM: [http://planetmath.org/?op=getobj&from=objects&id=6270 proof that L^p spaces are complete], id=6270 -- WP: [[Lp space]] -- Status: '''N''' ::[[User:AdamSmithee\|AdamSmithee]] 15:54, 3 February 2006 (UTC) ==46B50 Compactness in Banach (or normed) spaces== * PM: [http://planetmath.org/?op=getobj&from=objects&id=4457 proof of Schauder fixed point theorem], id=4457 -- WP guess: [[proof of Schauder fixed point theorem]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=~~4455~~4457 proof of Schauder fixed point theorem], id=~~4455~~4457 -- WP guess: [[proof of Schauder fixed point theorem]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=4455 Schauder fixed point theorem], id=4455 -- WP guess: [[Schauder fixed point theorem]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=8125 Tychonoff fixed point theorem], id=8125<sup style="color:red">new!</sup> -- WP guess: [[Tychonoff fixed point theorem]] -- Status: ==46B99 Miscellaneous== * PM: [http://planetmath.org/?op=getobj&from=objects&id=1929 \ell^p], id=1929 -- WP: [[Lp space]] -- Status: '''A''' :: [[User:Oleg Alexandrov\|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov\|talk]]) 19:52, 20 November 2005 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=5564 all norms on finite-dimensional vector spaces are equivalent], id=5564 -- WP guess: [[all norms on finite-dimensional vector spaces are equivalent]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=1605 Banach space], id=1605 -- WP guess: [[Banach space]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=6469 Banach-Steinhaus theorem], id=6469 -- WP: [[Banach-Steinhaus theorem]] -- Status: '''A''' Line 138 ⟶ 220: ::[[User:AdamSmithee\|AdamSmithee]] 10:25, 6 February 2006 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=4312 equivalent norms], id=4312 -- WP guess: [[equivalent norms]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=6633 every finite dimensional normed vector space is a Banach space], id=6633 -- WP guess: [[every finite dimensional normed vector space is a Banach space]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=6632 every subspace of a normed space of finite dimension is closed], id=6632 -- WP guess: [[every subspace of a normed space of finite dimension is closed]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=1604 normed vector space], id=1604 -- WP guess: [[normed vector space]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=6470 proof of Banach-Steinhaus theorem], id=6470 -- WP: [[Banach-Steinhaus theorem]] -- Status: '''A''' ::[[User:AdamSmithee\|AdamSmithee]] 10:25, 6 February 2006 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=7519 all norms are not equivalent], id=7519 -- WP guess: [[all norms are not equivalent]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=6703 extended norm], id=6703 -- WP guess: [[extended norm]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7458 scaling of the open ball in a normed vector space], id=7458 -- WP guess: [[scaling of the open ball in a normed vector space]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7092 shift operators in \ell^p], id=7092 -- WP guess: [[shift operators in \ell^p]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=9864 approximation property], id=9864<sup style="color:red">new!</sup> -- WP guess: [[approximation property]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=9751 necessary and sufficient conditions for a normed vector space to be a Banach space], id=9751<sup style="color:red">new!</sup> -- WP guess: [[necessary and sufficient conditions for a normed vector space to be a Banach space]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=9749 quotient norm], id=9749<sup style="color:red">new!</sup> -- WP guess: [[quotient norm]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=9750 quotients of Banach spaces by closed subspaces are Banach spaces under the quotient norm], id=9750<sup style="color:red">new!</sup> -- WP guess: [[quotients of Banach spaces by closed subspaces are Banach spaces under the quotient norm]] -- Status: ==46Bxx Normed linear spaces and Banach spaces; Banach lattices== ==46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)== * PM: [http://planetmath.org/?op=getobj&from=objects&id=3089 Bessel inequality], id=3089 -- WP: [[Bessel inequality]] -- Status: '''C''' ::[[User:Oleg Alexandrov\|Oleg Alexandrov]] 02:07, 5 March 2006 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=6364 direct integral of Hilbert spaces], id=6364 -- WP guess: [[direct integral of Hilbert spaces]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=6363 direct sum of Hilbert spaces], id=6363 -- WP guess: [[direct sum of Hilbert spaces]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=3401 Hilbert module], id=3401 -- WP guess: [[Hilbert module]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=6229 Hilbert parallelotope], id=6229 -- WP guess: [[Hilbert parallelotope]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=1930 Hilbert space], id=1930 -- WP guess: [[Hilbert space]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=3090 proof of Bessel inequality], id=3090 -- WP guess: [[proof of Bessel inequality]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=6239 Rellich selection theorem], id=6239 -- WP guess: [[Rellich selection theorem]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=5963 Riesz sequence], id=5963 -- WP ~~guess~~: [[Riesz sequence]] -- Status: '''C''' ::Along with [[Riesz basis]]. [[User:Bjcairns\|Ben Cairns]] 12:55, 18 April 2006 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=7271 \vert\langle Tv,v \rangle\vert \leq {\mu} \Vert v \Vert ^2 for all v implies \Vert T \Vert \leq {\mu}], id=7271 -- WP guess: [[\vert\langle Tv,v \rangle\vert \leq \mu \Vert v \Vert ^2 for all v implies \Vert T \Vert \leq \mu]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7691 example of non-separable Hilbert space], id=7691<sup style="color:red">new!</sup> -- WP guess: [[example of non-separable Hilbert space]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=8227 generalization of the parallelogram law], id=8227<sup style="color:red">new!</sup> -- WP guess: [[generalization of the parallelogram law]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=8228 Hlawka's inequality], id=8228<sup style="color:red">new!</sup> -- WP guess: [[Hlawka's inequality]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=8205 parallelogram law], id=8205<sup style="color:red">new!</sup> -- WP guess: [[parallelogram law]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=8229 proof of generalization of the parallelogram law], id=8229<sup style="color:red">new!</sup> -- WP guess: [[proof of generalization of the parallelogram law]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=8211 proof of parallelogram law], id=8211<sup style="color:red">new!</sup> -- WP guess: [[proof of parallelogram law]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7967 Schur's condition for a matrix to be a bounded operator on l^2], id=7967<sup style="color:red">new!</sup> -- WP guess: [[Schur's condition for a matrix to be a bounded operator on l^2]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=8214 yet another proof of parallelogram law], id=8214<sup style="color:red">new!</sup><sup style="color:red">new!</sup> -- WP guess: [[yet another proof of parallelogram law]] -- Status: ==46C15 Characterizations of Hilbert spaces== * PM: [http://planetmath.org/?op=getobj&from=objects&id=1933 classification of separable Hilbert spaces], id=1933 -- WP guess: [[classification of separable Hilbert spaces]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=~~6127 proof of~~1933 classification of separable Hilbert spaces], id=~~6127~~1933 -- WP guess: [[~~proof of~~ classification of separable Hilbert spaces]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=6127 proof of classification of separable Hilbert spaces], id=6127 -- WP guess: [[proof of classification of separable Hilbert spaces]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=8100 Banach spaces with complemented subspaces], id=8100<sup style="color:red">new!</sup> -- WP guess: [[Banach spaces with complemented subspaces]] -- Status: ==46C99 Miscellaneous== * PM: [http://planetmath.org/?op=getobj&from=objects&id=5969 characterization of tight frames in {\mathbb R}^n], id=5969 -- WP guess: [[characterization of tight frames in \mathbb R^n]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=~~5935~~5969 ~~frame~~characterization of tight frames in {\mathbb R}^n], id=~~5935~~5969 -- WP guess: [[~~frame~~characterization of tight frames in \mathbb R^n]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=~~5961~~5935 ~~multiresolution analysis~~frame], id=~~5961~~5935 -- WP guess: [[~~multiresolution analysis~~frame]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=5961 multiresolution analysis], id=5961 -- WP guess: [[multiresolution analysis]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=6130 proof of Riesz representation theorem for separable Hilbert spaces], id=6130 -- WP guess: [[Riesz representation theorem]] -- Status: '''N''' Line 187 ⟶ 311: ::[[User:AdamSmithee\|AdamSmithee]] 16:13, 3 February 2006 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=5586 Riesz-Fischer theorem], id=5586 -- WP guess: [[Riesz-Fischer theorem]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=5984 set of sampling], id=5984 -- WP guess: [[set of sampling]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=5959 wavelet], id=5959 -- WP guess: [[wavelet]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=5971 wavelet set], id=5971 -- WP guess: [[wavelet set]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=9448 Gabor frame], id=9448<sup style="color:red">new!</sup> -- WP guess: [[Gabor frame]] -- Status: ==46Cxx Inner product spaces and their generalizations, Hilbert spaces== ==46E15 Banach spaces of continuous, differentiable or analytic functions== * PM: [http://planetmath.org/?op=getobj&from=objects&id=2961 Ascoli-Arzelà theorem], id=2961 -- WP guess: [[Ascoli-Arzelà theorem]] -- Status: '''M''' :: [[User:Oleg Alexandrov\|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov\|talk]]) 06:57, 25 October 2005 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=3753 proof of Ascoli-ArzelÃ theorem], id=3753 -- WP guess: [[proof of Ascoli-ArzelÃ theorem]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=6146 proof of Stone-Weierstrass theorem], id=6146 -- WP guess: [[proof of Stone-Weierstrass theorem]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=2984 Stone-Weierstrass theorem], id=2984 -- WP guess: [[Stone-Weierstrass theorem]] -- Status: ==46E30 Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, KÃÂ¶the function spaces, Lorentz spaces, rearrangement invariant== * PM: [http://planetmath.org/?op=getobj&from=objects&id=2051 conjugate index], id=2051 -- WP guess: [[conjugate index]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=942051 ~~Holder~~conjugate ~~inequality~~index], id=942051 -- WP ~~guess~~: [[~~Holder~~conjugate ~~inequality~~index]] -- Status: '''C''' :: [[User:Oleg Alexandrov\|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov\|talk]]) 04:43, 11 March 2006 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=~~4110 proof of~~94 Holder inequality], id=~~4110~~94 -- WP guess: [[~~proof of~~ Holder inequality]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=~~4079~~4110 proof of ~~Young~~Holder ~~Inequality~~inequality], id=~~4079~~4110 -- WP guess: [[proof of ~~Young~~Holder ~~Inequality~~inequality]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=~~4078~~4079 proof of Young Inequality], id=~~4078~~4079 -- WP guess: [[proof of Young Inequality]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=4078 Young Inequality], id=4078 -- WP: [[Young's inequality]] -- Status: '''A''' :: [[User:Oleg Alexandrov\|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov\|talk]]) 04:10, 11 March 2006 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=7667 generalization of Young inequality], id=7667<sup style="color:red">new!</sup> -- WP guess: [[generalization of Young inequality]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=9170 generalized Hölder inequality], id=9170<sup style="color:red">new!</sup> -- WP guess: [[generalized Hölder inequality]] -- Status: ==46E35 Sobolev spaces and other spaces of ''smooth'' functions, embedding theorems, trace theorems== ~~==46E35 Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems==~~ * PM: [http://planetmath.org/?op=getobj&from=objects&id=6601 Sobolev space], id=6601 -- WP: [[Sobolev space]] -- Status: '''A''' :[[User:Oleg Alexandrov\|Oleg Alexandrov]] 22:50, 13 September 2005 (UTC) Line 222 ⟶ 359: * PM: [http://planetmath.org/?op=getobj&from=objects&id=6600 weak derivative], id=6600 -- WP: [[weak derivative]] -- Status: '''A''' :[[User:Oleg Alexandrov\|Oleg Alexandrov]] 22:50, 13 September 2005 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=6816 proof of Sobolev inequality for \Omega=\mathbf{R}^n], id=6816 -- WP guess: [[proof of Sobolev inequality for \Omega=\mathbfR^n]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=6812 Sobolev inequality], id=6812 -- WP guess: [[Sobolev inequality]] -- Status: ==46E40 Spaces of vector- and operator-valued functions== * PM: [http://planetmath.org/?op=getobj&from=objects&id=902 vector field], id=902 -- WP guess: [[vector field]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=902 vector field], id=902 -- WP guess: [[vector field]] -- Status: ==46Exx Linear function spaces and their duals== ==46F05 Topological linear spaces of test functions, distributions and ultradistributions== * PM: [http://planetmath.org/?op=getobj&from=objects&id=5655 example of Dirac sequence], id=5655 -- WP guess: [[example of Dirac sequence]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=~~4444~~5655 ~~space~~example of ~~rapidly~~Dirac ~~decreasing functions~~sequence], id=~~4444~~5655 -- WP guess: [[~~space~~example of ~~rapidly~~Dirac ~~decreasing functions~~sequence]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=4444 space of rapidly decreasing functions], id=4444 -- WP: [[Schwartz space]] -- Status: '''C''' ::[[User:Linas\|linas]] 21:44, 4 March 2006 (UTC) ==46F10 Operations with distributions== ==46Fxx Distributions, generalized functions, distribution spaces== ==46G05 Derivatives== * PM: [http://planetmath.org/?op=getobj&from=objects&id=2975 derivative], id=2975 -- WP guess: [[derivative]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=~~6395~~2975 ~~higher order derivatives of sine and cosine~~derivative], id=~~6395~~2975 -- WP guess: [[~~higher order derivatives of sine and cosine~~derivative]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=6395 higher order derivatives of sine and cosine], id=6395 -- WP guess: [[higher order derivatives of sine and cosine]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=8221 Fréchet derivative is unique], id=8221<sup style="color:red">new!</sup> -- WP guess: [[Fréchet derivative is unique]] -- Status: ==46Gxx Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces)== ==46H05 General theory of topological algebras== * PM: [http://planetmath.org/?op=getobj&from=objects&id=3333 Banach algebra], id=3333 -- WP guess: [[Banach algebra]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=3333 Banach algebra], id=3333 -- WP guess: [[Banach algebra]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7021 Hilbert spaces are uniformly convex spaces], id=7021 -- WP guess: [[ Hilbert spaces are uniformly convex spaces]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7026 Banach-Krein-mulian theorem], id=7026 -- WP guess: [[Banach-Krein-Mulian theorem]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7034 Hahn-Banach theorem(geometric form)], id=7034 -- WP guess: [[Hahn-Banach theorem (geometric form)]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7035 Hyperplane], id=7035 -- WP guess: [[Hyperplane]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7167 proof of Hilbert space is uniformly convex space], id=7167 -- WP guess: [[proof of Hilbert space is uniformly convex space]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7011 Property of uniformly convex Banach Space], id=7011 -- WP guess: [[Property of uniformly convex Banach Space]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=6983 Uniformly convex Banach space], id=6983 -- WP guess: [[Uniformly convex Banach space]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7028 uniformly convex space is reflexive], id=7028 -- WP guess: [[uniformly convex space is reflexive]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=9743 Gelfand transform], id=9743<sup style="color:red">new!</sup> -- WP guess: [[Gelfand transform]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=9871 Gelfand-Mazur theorem], id=9871<sup style="color:red">new!</sup><sup style="color:red">new!</sup> -- WP guess: [[Gelfand-Mazur theorem]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=9757 invertible elements in a Banach algebra form an open set], id=9757<sup style="color:red">new!</sup> -- WP guess: [[invertible elements in a Banach algebra form an open set]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=9737 multiplicative linear functional], id=9737<sup style="color:red">new!</sup> -- WP guess: [[multiplicative linear functional]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=9756 Neumann series in Banach algebras], id=9756<sup style="color:red">new!</sup> -- WP guess: [[Neumann series in Banach algebras]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=8286 normed algebra], id=8286<sup style="color:red">new!</sup> -- WP guess: [[normed algebra]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=8141 rotund space], id=8141<sup style="color:red">new!</sup> -- WP guess: [[rotund space]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=9791 spectrum is a non-empty compact set], id=9791<sup style="color:red">new!</sup> -- WP guess: [[spectrum is a non-empty compact set]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=8299 topological divisor of zero], id=8299<sup style="color:red">new!</sup> -- WP guess: [[topological divisor of zero]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=8295 topologically nilpotent], id=8295<sup style="color:red">new!</sup> -- WP guess: [[topologically nilpotent]] -- Status: ==46H15 Representations of topological algebras== * PM: [http://planetmath.org/?op=getobj&from=objects&id=9843 Banach -algebra representation], id=9843<sup style="color:red">new!</sup> -- WP guess: [[Banach -algebra representation]] -- Status: ==46H35 Topological algebras of operators== * PM: [http://planetmath.org/?op=getobj&from=objects&id=6402 topological -algebra], id=6402 -- WP guess: [[topological -algebra]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=6402 topological -algebra], id=6402 -- WP guess: [[topological -algebra]] -- Status: ==46Hxx Topological algebras, normed rings and algebras, Banach algebras== ==46J10 Banach algebras of continuous functions, function algebras== ==46Jxx Commutative Banach algebras and commutative topological algebras== ==46K05 General theory of topological algebras with involution== ==46K10 Representations of topological algebras with involution== * PM: [http://planetmath.org/?op=getobj&from=objects&id=9845 criterion for a Banach -algebra representation to be irreducible], id=9845<sup style="color:red">new!</sup> -- WP guess: [[criterion for a Banach -algebra representation to be irreducible]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=9844 representations of Banach -algebras are continuous], id=9844<sup style="color:red">new!</sup> -- WP guess: [[representations of Banach -algebras are continuous]] -- Status: ==46Kxx Topological (rings and) algebras with an involution== ==46L05 General theory of $C^$-algebras== PM: [http://planetmath.org/?op=getobj&from=objects&id=3334 C^-algebra], id=3334 -- WP: [[C-algebra]] -- Status: '''A''' :: [[User:Oleg Alexandrov\|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov\|talk]]) 23:00, 10 December 2005 (UTC) Line 250 ⟶ 463: :: Our article contains the relevant bit of info. The proof itself which is contained in the PM article, is not wanted. [[User:Oleg Alexandrov\|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov\|talk]]) 23:02, 10 December 2005 (UTC) * PM: [http://planetmath.org/?op=getobj&from=objects&id=3335 Gelfand-Naimark representation theorem], id=3335 -- WP guess: [[Gelfand-Naimark representation theorem]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=4574 state], id=4574 -- WP guess: [[state]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=9807 example of Banach algebra which is not a C^-algebra for any involution], id=9807<sup style="color:red">new!</sup> -- WP guess: [[example of Banach algebra which is not a C^-algebra for any involution]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=9862 special elements in a C^-algebra and their spectral properties], id=9862<sup style="color:red">new!</sup><sup style="color:red">new!</sup> -- WP guess: [[special elements in a C^-algebra and their spectral properties]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=9846 topologically irreducible representations are algebrically irreducible for C^-algebras], id=9846<sup style="color:red">new!</sup> -- WP guess: [[topologically irreducible representations are algebrically irreducible for C^-algebras]] -- Status: ==46L10 General theory of von Neumann algebras== * PM: [http://planetmath.org/?op=getobj&from=objects&id=9868 polar decomposition in von Neumann algebras], id=9868<sup style="color:red">new!</sup> -- WP guess: [[polar decomposition in von Neumann algebras]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=9722 von Neumann algebra], id=9722<sup style="color:red">new!</sup> -- WP guess: [[von Neumann algebra]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=9869 von Neumann algebras contain the range projections of its elements], id=9869<sup style="color:red">new!</sup> -- WP guess: [[von Neumann algebras contain the range projections of its elements]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=9870 von Neumann algebras of dimension greater than one contain non-trivial projections], id=9870<sup style="color:red">new!</sup> -- WP guess: [[von Neumann algebras of dimension greater than one contain non-trivial projections]] -- Status: ==46L65 Quantizations, deformations== * PM: [http://planetmath.org/?op=getobj&from=objects&id=7540 Quantization], id=7540 -- WP guess: [[Quantization]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=7894 canonical quantization], id=7894<sup style="color:red">new!</sup> -- WP guess: [[canonical quantization]] -- Status: ==46L85 Noncommutative topology== * PM: [http://planetmath.org/?op=getobj&from=objects&id=4065 Gelfand-Naimark theorem], id=4065 -- WP: [[Gelfand-Naimark theorem]] -- Status: '''A''' :: Ours is more elementary and more complete. [[User:Oleg Alexandrov\|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov\|talk]]) 23:03, 10 December 2005 (UTC) Line 261 ⟶ 497: ==46L87 Noncommutative differential geometry== * PM: [http://planetmath.org/?op=getobj&from=objects&id=3329 Fredholm module], id=3329 -- WP guess: [[Fredholm module]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=3329 Fredholm module], id=3329 -- WP guess: [[Fredholm module]] -- Status: ==46Lxx Selfadjoint operator algebras ($C^$-algebras, von Neumann ($W$-) algebras, etc.)== ==46M05 Tensor products== * PM: [http://planetmath.org/?op=getobj&from=objects&id=899 triple scalar product], id=899 -- WP guess: [[triple scalar product]] -- Status: * PM: [http://planetmath.org/?op=getobj&from=objects&id=899 triple scalar product], id=899 -- WP guess: [[triple scalar product]] -- Status: ==46Mxx Methods of category theory in functional analysis== ==46N99 Miscellaneous== * PM: [http://planetmath.org/?op=getobj&from=objects&id=9629 Schwarzian derivative], id=9629<sup style="color:red">new!</sup> -- WP guess: [[Schwarzian derivative]] -- Status: ==46Nxx Miscellaneous applications of functional analysis== ==46T12 Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds== * PM: [http://planetmath.org/?op=getobj&from=objects&id=1700 path integral], id=1700 -- WP guess: [[path integral]] -- Status: ==46T20 Continuous and differentiable maps== ==46Txx Nonlinear functional analysis==