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

Revision as of 20:08, 9 September 2005

Revision as of 01:43, 5 March 2006

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

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

* PM: [http://planetmath.org/?op=getobj&from=objects&id=4321 Baker-Campbell-Hausdorff formula(e)], id=4321 -- WP: [[Baker-Campbell-Hausdorff formula]] -- Status: '''A'''

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* PM: [http://planetmath.org/?op=getobj&from=objects&id=4526 closed operator], id=4526 -- WP: [[closed operator]] -- Status: '''C'''

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

* PM: [http://planetmath.org/?op=getobj&from=objects&id=4523 densely defined], id=4523 -- WP guess: [[densely defined]] -- Status:

* PM: [http://planetmath.org/?op=getobj&from=objects&id=4524 properties of the adjoint operator], id=4524 -- WP guess: [[properties of the adjoint operator]] -- Status:

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

==47A35 Ergodic theory==

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

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

* PM: [http://planetmath.org/?op=getobj&from=objects&id=3353 Fredholm operator], id=3353 -- WP guess: [[Fredholm operator]] -- Status: '''A'''

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

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==47A55 Perturbation theory==

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

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

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

* PM: [http://planetmath.org/?op=getobj&from=objects&id=45272092 selfEuler-adjointLagrange operatordifferential equation (elementary)], id=45272092 -- WP guess: [[selfEuler-adjointLagrange operatordifferential equation (elementary)]] -- Status:

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

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

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

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

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

* PM: [http://planetmath.org/?op=getobj&from=objects&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&from=objects&id=65636564 proof of basic criterion for self-adjointness], id=65636564 -- WP guess: [[proof of basic criterion for self-adjointness]] -- Status:

==47C05 Operators in algebras==

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

==47G30 Pseudodifferential operators==

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

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

==47H10 Fixed-point theorems==

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

* PM: [http://planetmath.org/?op=getobj&from=objects&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&from=objects&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:

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

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

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

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

* PM: [http://planetmath.org/?op=getobj&from=objects&id=20133018 Beltramioperator identitynorm], id=20133018 -- WP guess: [[Beltramioperator identitynorm]] -- Status:

==47S99 Miscellaneous==

* PM: [http://planetmath.org/?op=getobj&from=objects&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)