Wikipedia:WikiProject Mathematics/PlanetMath Exchange/46-XX Functional analysis: Difference between revisions
Content deleted Content added
Adding new PlanetMath entries. |
|||
Line 50:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=4528 symmetric set], id=4528 -- WP guess: [[symmetric set]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=7453 balanced set], id=7453<sup><font color=red>new!</font></sup> -- 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<sup><font color=red>new!</font></sup> -- 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<sup><font color=red>new!</font></sup> -- WP guess: [[cone]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=6723 weak convergence], id=6723<sup><font color=red>new!</font></sup> -- WP guess: [[weak convergence]] -- Status:
==46A03 General theory of locally convex spaces==
Line 55 ⟶ 63:
* 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<sup><font color=red>new!</font></sup> -- WP guess: [[proof of Krein-Milman theorem]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=6855 weak-* topology], id=6855<sup><font color=red>new!</font></sup> -- WP guess: [[weak-* topology]] -- Status:
==46A08 Barrelled spaces, bornological spaces==
==46A30 Open mapping and closed graph theorems; completeness (including $B$-, $B r$-completeness)==
Line 72 ⟶ 86:
* 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<sup><font color=red>new!</font></sup> -- WP guess: [[conical neighborhood]] -- Status:
==46A99 Miscellaneous==
Line 82 ⟶ 98:
* 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<sup><font color=red>new!</font></sup> -- WP guess: [[proof of Heine-Cantor theorem]] -- Status:
==46B03 Isomorphic theory (including renorming) of Banach spaces==
Line 98 ⟶ 116:
* 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<sup><font color=red>new!</font></sup> -- WP guess: [[Proof of Banach-Alaoglu theorem]] -- Status:
==46B20 Geometry and structure of normed linear spaces==
Line 117 ⟶ 137:
* 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<sup><font color=red>new!</font></sup> -- WP guess: [[sub-linear]] -- Status:
==46B25 Classical Banach spaces in the general theory==
Line 160 ⟶ 182:
* 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<sup><font color=red>new!</font></sup> -- WP guess: [[all norms are not equivalent]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=6703 extended norm], id=6703<sup><font color=red>new!</font></sup> -- 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<sup><font color=red>new!</font></sup> -- 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<sup><font color=red>new!</font></sup> -- WP guess: [[shift operators in \ell^p]] -- Status:
==46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)==
Line 181 ⟶ 211:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=5963 Riesz sequence], id=5963 -- WP guess: [[Riesz sequence]] -- Status:
* 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<sup><font color=red>new!</font></sup> -- WP guess: [[\vert\langle Tv,v \rangle\vert \leq \mu \Vert v \Vert ^2 for all v implies \Vert T \Vert \leq \mu]] -- Status:
==46C15 Characterizations of Hilbert spaces==
Line 240 ⟶ 272:
* 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<sup><font color=red>new!</font></sup> -- 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<sup><font color=red>new!</font></sup> -- WP guess: [[Sobolev inequality]] -- Status:
==46E40 Spaces of vector- and operator-valued functions==
Line 261 ⟶ 297:
* 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<sup><font color=red>new!</font></sup> -- 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<sup><font color=red>new!</font></sup> -- WP guess: [[Banach-Krein-mulian theorem]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=7034 Hahn-Banach theorem(geometric form)], id=7034<sup><font color=red>new!</font></sup> -- WP guess: [[Hahn-Banach theorem(geometric form)]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=7035 Hyperplane], id=7035<sup><font color=red>new!</font></sup> -- WP guess: [[Hyperplane]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=7167 proof of Hilbert space is uniformly convex space], id=7167<sup><font color=red>new!</font></sup> -- 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<sup><font color=red>new!</font></sup> -- 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<sup><font color=red>new!</font></sup> -- WP guess: [[Uniformly convex Banach space]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=7028 uniformly convex space is reflexive], id=7028<sup><font color=red>new!</font></sup> -- WP guess: [[uniformly convex space is reflexive]] -- Status:
==46H35 Topological algebras of operators==
Line 279 ⟶ 331:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=4574 state], id=4574 -- WP guess: [[state]] -- Status:
==46L65 Quantizations, deformations==
* PM: [http://planetmath.org/?op=getobj&from=objects&id=7540 Quantization], id=7540<sup><font color=red>new!</font></sup> -- WP guess: [[Quantization]] -- Status:
==46L85 Noncommutative topology==
Line 298 ⟶ 354:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=1700 path integral], id=1700 -- WP guess: [[path integral]] -- Status:
==46T20 Continuous and differentiable maps==
| |||