Wikipedia:WikiProject Mathematics/PlanetMath Exchange/47-XX Operator theory
From Wikipedia, the free encyclopedia
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:
- PM : The first field is the link to the PlanetMath article, along with the article's object ID.
- 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.
- 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.
- if the WP field is correct please remove the qualifier "guess".
- If the corresponding Wikipedia article exists, but the link to it is wrong, please fix the link.
- If you copy or merge an article from PlanetMath, please update the WP and Status fields for that entry.
- If you have any comments, for example, thoughts on how the PlanetMath article compares to the corresponding Wikipedia article(s), please place such comments on a new indented line following the entry. Comments of this kind are very valuable.
Don't forget to include the relevant template if you copy over text or feel like an external link is warranted
- {{planetmath|id=|title=}} for copied over text
- {{planetmath reference|id=|title=}} for an external link
See the main page for examples and usage criteria.
One can use the web-based program Pmform to convert PlanetMath articles to the Wikipedia format. As a side benefit, this tool will place the PlanetMath template for you.
[edit] 47-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
- PM: operator topologies, id=9729new! -- WP guess: operator topologies -- Status:
[edit] 47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
- 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:
[edit] 47A07 Forms (bilinear, sesquilinear, multilinear)
[edit] 47A10 Spectrum, resolvent
[edit] 47A12 Numerical range, numerical radius
- PM: Dunkl-Williams inequality, id=9212new! -- WP guess: Dunkl-Williams inequality -- Status:
[edit] 47A15 Invariant subspaces
[edit] 47A35 Ergodic theory
[edit] 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)
[edit] 47A55 Perturbation theory
- PM: Kato-Rellich theorem, id=6562 -- WP guess: Kato-Rellich theorem -- Status:
[edit] 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:
[edit] 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:
[edit] 47Axx General theory of linear operators
[edit] 47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.)
- PM: self-adjoint operator, id=4527 -- WP guess: self-adjoint operator -- Status:
[edit] 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:
[edit] 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:
[edit] 47Bxx Special classes of linear operators
[edit] 47C05 Operators in algebras
- PM: functional calculus for Hermitian matrices, id=6271 -- WP guess: functional calculus -- Status:
[edit] 47C10 Operators in $^*$-algebras
- PM: partial isometry, id=7830new! -- WP guess: partial isometry -- Status:
[edit] 47C15 Operators in $C^*$- or von Neumann algebras
[edit] 47Cxx Individual linear operators as elements of algebraic systems
[edit] 47G30 Pseudodifferential operators
- PM: Dini derivative, id=4714 -- WP: Dini derivative -- Status: C
-
- Oleg Alexandrov 3 July 2005 20:09 (UTC)
[edit] 47Gxx Integral, integro-differential, and pseudodifferential operators
[edit] 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:
[edit] 47Hxx Nonlinear operators and their properties
[edit] 47J07 Abstract inverse mapping and implicit function theorems
[edit] 47Jxx Equations and inequalities involving nonlinear operators
[edit] 47L07 Convex sets and cones of operators
[edit] 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:
[edit] 47Lxx Linear spaces and algebras of operators
[edit] 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: