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

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

 * PM: operator topologies, id=9729new! -- WP guess: operator topologies -- Status:

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

 * PM: adjoint, id=4522 -- WP guess: adjoint -- Status:


 * PM: Baker-Campbell-Hausdorff formula(e), id=4321 -- WP: Baker-Campbell-Hausdorff formula -- Status: A
 * WP article looks reasonable. Oleg Alexandrov 15:27, 9 September 2005 (UTC)


 * PM: closed operator, id=4526 -- WP: closed operator -- Status: C
 * Oleg Alexandrov 19:58, 9 September 2005 (UTC)


 * PM: densely defined, id=4523 -- WP guess: densely defined -- Status:


 * PM: properties of the adjoint operator, id=4524 -- WP guess: properties of the adjoint operator -- Status:


 * PM: polar decomposition, id=8075new! -- WP guess: polar decomposition -- Status:

47A12 Numerical range, numerical radius

 * PM: Dunkl-Williams inequality, id=9212new! -- WP guess: Dunkl-Williams inequality -- Status:

47A53 (Semi-) Fredholm operators; index theories

 * PM: Fredholm index, id=3863 -- WP: Fredholm index -- Status: A


 * PM: Fredholm operator, id=3353 -- WP guess: Fredholm operator -- Status: A


 * PM: 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. Oleg Alexandrov 15:26, 9 September 2005 (UTC)

47A55 Perturbation theory

 * PM: 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: Taylor's formula for matrix functions, id=4311 -- WP guess: Taylor's formula for matrix functions -- Status:

47A60 Functional calculus

 * PM: Beltrami identity, id=2013 -- WP guess: Beltrami identity -- Status:


 * PM: calculus of variations, id=1995 -- WP guess: calculus of variations -- Status:


 * PM: derivation of Euler-Lagrange differential equation (advanced), id=6393 -- WP guess: derivation of Euler-Lagrange differential equation (advanced) -- Status:


 * PM: derivation of Euler-Lagrange differential equation (elementary), id=6401 -- WP guess: derivation of Euler-Lagrange differential equation (elementary) -- Status:


 * PM: Euler-Lagrange differential equation (advanced), id=6400 -- WP guess: Euler-Lagrange differential equation (advanced) -- Status:


 * PM: Euler-Lagrange differential equation (elementary), id=2092 -- WP guess: Euler-Lagrange differential equation (elementary) -- Status:


 * PM: stationary point, id=7457 -- WP guess: stationary point -- Status:


 * PM: Russo-Dye theorem, id=8074new! -- WP guess: Russo-Dye theorem -- Status:

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

 * PM: self-adjoint operator, id=4527 -- WP guess: self-adjoint operator -- Status:

47B25 Symmetric and selfadjoint operators (unbounded)

 * PM: basic criterion for self-adjointness, id=6563 -- WP guess: basic criterion for self-adjointness -- Status:


 * PM: 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: multiplication operator on L^2, id=7654new! -- WP guess: multiplication operator on L^2 -- Status:


 * PM: operator norm of multiplication operator on L^2, id=7798new! -- WP guess: operator norm of multiplication operator on L^2 -- Status:

47C05 Operators in algebras

 * PM: functional calculus for Hermitian matrices, id=6271 -- WP guess: functional calculus -- Status:

47C10 Operators in $^*$-algebras

 * PM: partial isometry, id=7830new! -- WP guess: partial isometry -- Status:

47G30 Pseudodifferential operators

 * PM: Dini derivative, id=4714 -- WP: Dini derivative -- Status: C
 * Oleg Alexandrov 3 July 2005 20:09 (UTC)

47H10 Fixed-point theorems

 * PM: 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: Brouwer fixed point in one dimension, id=4480 -- WP guess: Brouwer fixed point in one dimension -- Status:


 * PM: Brouwer fixed point theorem, id=3046 -- WP guess: Brouwer fixed point theorem -- Status:


 * PM: fixed point property, id=4704 -- WP guess: fixed point property -- Status:


 * PM: proof of Brouwer fixed point theorem, id=3642 -- WP guess: proof of Brouwer fixed point theorem -- Status:


 * PM: KKM lemma, id=8597new! -- WP guess: KKM lemma -- Status:


 * PM: the topologist's sine curve has the fixed point property, id=9274new! -- WP guess: the topologist's sine curve has the fixed point property -- Status:

47L25 Operator spaces (= matricially normed spaces)

 * PM: operator norm, id=3018 -- WP guess: operator norm -- Status:


 * PM: examples of bounded and unbounded operators, id=7091 -- WP: examples of bounded and unbounded operators -- Status: A
 * Oleg Alexandrov (talk) 04:36, 10 March 2006 (UTC)


 * PM: derivative operator is unbounded in the sup norm, id=7732new! -- WP guess: derivative operator is unbounded in the sup norm -- Status:

47S99 Miscellaneous

 * PM: 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. Oleg Alexandrov 20:08, 9 September 2005 (UTC)


 * PM: matrix inversion lemma, id=7577 -- WP guess: matrix inversion lemma -- Status: