Wikipedia:WikiProject Mathematics/PlanetMath Exchange/47-XX Operator theory: Difference between revisions

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{{Planetmath instructions|topic=47-XX Operator theory}}

==47-00 General reference works (handbooks, dictionaries, bibliographies, etc.)==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=30189729 operator normtopologies], id=30189729^{<span style="color:red;">new!</span>} -- WP guess: [[operator normtopologies]] -- Status:

==47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=4522 adjoint], id=4522 -- WP guess: [[adjoint]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=43214522 Baker-Campbell-Hausdorff formula(e)adjoint], id=43214522 -- WP guess: [[Baker-Campbell-Hausdorff formula(e)adjoint]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=45264321 closedBaker-Campbell-Hausdorff operatorformula(e)], id=45264321 -- WP guess: [[closedBaker-Campbell-Hausdorff operatorformula]] -- Status: '''A'''

:: WP article looks reasonable. [[User:Oleg Alexandrov|Oleg Alexandrov]] 15:27, 9 September 2005 (UTC)

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=45234526 denselyclosed definedoperator], id=45234526 -- WP guess: [[denselyclosed definedoperator]] -- Status: '''C'''

::[[User:Oleg Alexandrov|Oleg Alexandrov]] 19:58, 9 September 2005 (UTC)

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=45244523 propertiesdensely of the adjoint operatordefined], id=45244523 -- WP guess: [[propertiesdensely of the adjoint operatordefined]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=45274524 properties of the self-adjoint operator], id=45274524 -- WP guess: [[self-properties of the adjoint operator]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=47388075 Drazinpolar inversedecomposition], id=47388075^{<span style="color:red;">new!</span>} -- WP guess: [[Drazinpolar inversedecomposition]] -- Status:

==47A07 Forms (bilinear, sesquilinear, multilinear)==

==47A10 Spectrum, resolvent==

==47A12 Numerical range, numerical radius==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=65629212 KatoDunkl-RellichWilliams theoreminequality], id=65629212^{<span style="color:red;">new!</span>} -- WP guess: [[KatoDunkl-RellichWilliams theoreminequality]] -- Status:

==47A15 Invariant subspaces==

==47A35 Ergodic theory==

==47A53 (Semi-) Fredholm operators; index theories==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=3863 Fredholm index], id=3863 -- WP guess: [[Fredholm index]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=33533863 Fredholm operatorindex], id=33533863 -- WP guess: [[Fredholm operatorindex]] -- Status: '''A'''

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=57373353 semi-Fredholm operator], id=57373353 -- WP guess: [[semi-Fredholm operator]] -- Status: '''A'''

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=5737 semi-Fredholm operator], id=5737 -- WP: [[semi-Fredholm operator]] -- Status: '''N'''

:: The PM article is a barebone definition. I would not be willing to create an article for that. [[User:Oleg Alexandrov|Oleg Alexandrov]] 15:26, 9 September 2005 (UTC)

==47A55 Perturbation theory==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=6562 Kato-Rellich theorem], id=6562 -- WP guess: [[Kato-Rellich theorem]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=6562 Kato-Rellich theorem], id=6562 -- WP guess: [[Kato-Rellich theorem]] -- Status:

==47A56 Functions whose values are linear operators (operator and matrix valued functions, etc., including analytic and meromorphic ones==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=4311 Taylor's formula for matrix functions], id=4311 -- WP guess: [[Taylor's formula for matrix functions]] -- Status:

==47A60 Functional calculus==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=2013 Beltrami identity], id=2013 -- WP guess: [[Beltrami identity]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=19952013 calculusBeltrami of variationsidentity], id=19952013 -- WP guess: [[calculusBeltrami of variationsidentity]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=63931995 derivationcalculus of Euler-Lagrange differential equation (advanced)variations], id=63931995 -- WP guess: [[derivationcalculus of Euler-Lagrange differential equation (advanced)variations]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=64016393 derivation of Euler-Lagrange differential equation (elementaryadvanced)], id=64016393 -- WP guess: [[derivation of Euler-Lagrange differential equation (elementaryadvanced)]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=64006401 derivation of Euler-Lagrange differential equation (advancedelementary)], id=64006401 -- WP guess: [[derivation of Euler-Lagrange differential equation (advancedelementary)]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=20926400 Euler-Lagrange differential equation (elementaryadvanced)], id=20926400 -- WP guess: [[Euler-Lagrange differential equation (elementaryadvanced)]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=65632092 basicEuler-Lagrange criteriondifferential forequation self-adjointness(elementary)], id=65632092 -- WP guess: [[basicEuler-Lagrange criteriondifferential forequation self-adjointness(elementary)]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=20137457 Beltramistationary identitypoint], id=20137457 -- WP guess: [[Beltramistationary identitypoint]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=8074 Russo-Dye theorem], id=8074^{<span style="color:red;">new!</span>} -- WP guess: [[Russo-Dye theorem]] -- Status:

==47Axx General theory of linear operators==

==47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.)==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=4527 self-adjoint operator], id=4527 -- WP guess: [[self-adjoint operator]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=45224527 self-adjoint operator], id=45224527 -- WP guess: [[self-adjoint operator]] -- Status:

==47B25 Symmetric and selfadjoint operators (unbounded)==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=6563 basic criterion for self-adjointness], id=6563 -- WP guess: [[basic criterion for self-adjointness]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=6564 proof of6563 basic criterion for self-adjointness], id=65646563 -- WP guess: [[proof of basic criterion for self-adjointness]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=6564 proof of basic criterion for self-adjointness], id=6564 -- WP guess: [[proof of basic criterion for self-adjointness]] -- Status:

==47B38 Operators on function spaces (general)==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=7654 multiplication operator on L^2], id=7654^{<span style="color:red;">new!</span>} -- WP guess: [[multiplication operator on L^2]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=62717798 functionaloperator calculusnorm forof Hermitianmultiplication matricesoperator on L^2], id=62717798^{<span style="color:red;">new!</span>} -- WP guess: [[functionaloperator calculusnorm forof Hermitianmultiplication matricesoperator on L^2]] -- Status:

==47Bxx Special classes of linear operators==

==47C05 Operators in algebras==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=6271 functional calculus for Hermitian matrices], id=6271 -- WP guess: [[functional calculus for Hermitian matrices]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=6271 functional calculus for Hermitian matrices], id=6271 -- WP guess: [[functional calculus]] -- Status:

==47C10 Operators in $^*$-algebras==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=7830 partial isometry], id=7830^{<span style="color:red;">new!</span>} -- WP guess: [[partial isometry]] -- Status:

==47C15 Operators in $C^*$- or von Neumann algebras==

==47Cxx Individual linear operators as elements of algebraic systems==

==47G30 Pseudodifferential operators==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=4714 Dini derivative], id=4714 -- WP: [[Dini derivative]] -- Status: '''C'''

:: [[User:Oleg Alexandrov|Oleg Alexandrov]] 3 July 2005 20:09 (UTC)

==47Gxx Integral, integro-differential, and pseudodifferential operators==

==47H10 Fixed-point theorems==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=4705 any topological space with the fixed point property is connected], id=4705 -- WP guess: [[any topological space with the fixed point property is connected]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=44804705 Brouwerany topological space with the fixed point inproperty oneis dimensionconnected], id=44804705 -- WP guess: [[Brouwerany topological space with the fixed point inproperty oneis dimensionconnected]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=30464480 Brouwer fixed point theoremin one dimension], id=30464480 -- WP guess: [[Brouwer fixed point theoremin one dimension]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=47043046 Brouwer fixed point propertytheorem], id=47043046 -- WP guess: [[Brouwer fixed point propertytheorem]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=3642 proof of Brouwer4704 fixed point theoremproperty], id=36424704 -- WP guess: [[proof of Brouwer fixed point theoremproperty]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=47053642 anyproof topologicalof space with theBrouwer fixed point property is connectedtheorem], id=47053642 -- WP guess: [[anyproof topologicalof space with theBrouwer fixed point property is connectedtheorem]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=8597 KKM lemma], id=8597^{<span style="color:red;">new!</span>} -- WP guess: [[KKM lemma]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=9274 the topologist's sine curve has the fixed point property], id=9274^{<span style="color:red;">new!</span>} -- WP guess: [[the topologist's sine curve has the fixed point property]] -- Status:

==47Hxx Nonlinear operators and their properties==

==47J07 Abstract inverse mapping and implicit function theorems==

==47Jxx Equations and inequalities involving nonlinear operators==

==47L07 Convex sets and cones of operators==

==47L25 Operator spaces (= matricially normed spaces)==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=3018 operator norm], id=3018 -- WP guess: [[operator norm]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=38633018 Fredholmoperator indexnorm], id=38633018 -- WP guess: [[Fredholmoperator indexnorm]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=7091 examples of bounded and unbounded operators], id=7091 -- WP: [[examples of bounded and unbounded operators]] -- Status: '''A'''

:: [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 04:36, 10 March 2006 (UTC)

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=7732 derivative operator is unbounded in the sup norm], id=7732^{<span style="color:red;">new!</span>} -- WP guess: [[derivative operator is unbounded in the sup norm]] -- Status:

==47Lxx Linear spaces and algebras of operators==

==47S99 Miscellaneous==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=4738 Drazin inverse], id=4738 -- WP guess: [[Drazin inverse]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=4738 Drazin inverse], id=4738 -- WP: [[Drazin inverse]] -- Status: '''N'''

:Just a definition of a rather obscure kind of inverse for operators which are not normally invertible. [[User:Oleg Alexandrov|Oleg Alexandrov]] 20:08, 9 September 2005 (UTC)

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=7577 matrix inversion lemma], id=7577 -- WP guess: [[matrix inversion lemma]] -- Status:

==47Sxx Other (nonclassical) types of operator theory==