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&from=objects&id=9729 operator topologies], id=9729<sup><span style="color:red;">new!</span></sup> -- WP guess: [[operator topologies]] -- Status:
==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
:: WP article looks reasonable. [[User:Oleg Alexandrov|Oleg Alexandrov]] 15:27, 9 September 2005 (UTC)
* PM: [http://planetmath.org/?op=getobj&from=objects&id=4526 closed operator], id=4526 -- WP
::[[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:
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* 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:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=
==47A07 Forms (bilinear, sesquilinear, multilinear)==
==47A10 Spectrum, resolvent==
==47A12 Numerical range, numerical radius==
* PM: [http://planetmath.org/?op=getobj&from=objects&id=
==47A15 Invariant subspaces==
==47A35 Ergodic theory==
==47A53 (Semi-) Fredholm operators; index theories==
* PM: [http://planetmath.org/?op=getobj&from=objects&id=
* 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
:: 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&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:
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* PM: [http://planetmath.org/?op=getobj&from=objects&id=2092 Euler-Lagrange differential equation (elementary)], id=2092 -- WP guess: [[Euler-Lagrange differential equation (elementary)]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=7457 stationary point], id=7457 -- WP guess: [[stationary point]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=8074 Russo-Dye theorem], id=8074<sup><span style="color:red;">new!</span></sup> -- 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&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 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&from=objects&id=7654 multiplication operator on L^2], id=7654<sup><span style="color:red;">new!</span></sup> -- WP guess: [[multiplication operator on L^2]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=7798 operator norm of multiplication operator on L^2], id=7798<sup><span style="color:red;">new!</span></sup> -- WP guess: [[operator norm of multiplication operator on L^2]] -- Status:
==47Bxx Special classes of linear operators==
==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:
==47C10 Operators in $^*$-algebras==
* PM: [http://planetmath.org/?op=getobj&from=objects&id=7830 partial isometry], id=7830<sup><span style="color:red;">new!</span></sup> -- 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&from=objects&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&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:
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* PM: [http://planetmath.org/?op=getobj&from=objects&id=3642 proof of Brouwer fixed point theorem], id=3642 -- WP guess: [[proof of Brouwer fixed point theorem]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=8597 KKM lemma], id=8597<sup><span style="color:red;">new!</span></sup> -- WP guess: [[KKM lemma]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&id=9274 the topologist's sine curve has the fixed point property], id=9274<sup><span style="color:red;">new!</span></sup> -- 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&from=objects&id=3018 operator norm], id=3018 -- WP guess: [[operator norm]] -- Status:
* PM: [http://planetmath.org/?op=getobj&from=objects&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&from=objects&id=7732 derivative operator is unbounded in the sup norm], id=7732<sup><span style="color:red;">new!</span></sup> -- 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&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)
* PM: [http://planetmath.org/?op=getobj&from=objects&id=7577 matrix inversion lemma], id=7577 -- WP guess: [[matrix inversion lemma]] -- Status:
==47Sxx Other (nonclassical) types of operator theory==
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