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

This page provides a list of all articles available at PlanetMath in the following topic:

47-XX Operator theory.

This list will be periodically updated. Each entry in the list has three fields:

1. PM : The first field is the link to the PlanetMath article, along with the article's object ID.
2. WP : The second field is either a "guessed" link to a correspondingly named Wikipedia article, produced by the script which generated the list, or one or more manually entered links to the corresponding Wikipedia articles on the subject.
3. Status : The third field is the status field, which explains the current status of the entry. The recommended status entries are:

Status	means PM article
N	not needed
A	adequately covered
C	copied
M	merged
NC	needs copying
NM	needs merging

• Please update the WP and Status fields as appropriate.
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47-00 General reference works (handbooks, dictionaries, bibliographies, etc.)

• PM: operator topologies, id=9729^new! -- 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=8075^new! -- WP guess: polar decomposition -- Status:

47A12 Numerical range, numerical radius

• PM: Dunkl-Williams inequality, id=9212^new! -- 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=8074^new! -- 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=7654^new! -- WP guess: multiplication operator on L^2 -- Status:

• PM: operator norm of multiplication operator on L^2, id=7798^new! -- 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=7830^new! -- 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=8597^new! -- WP guess: KKM lemma -- Status:

• PM: the topologist's sine curve has the fixed point property, id=9274^new! -- 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=7732^new! -- 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: