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:
- 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.
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- {{planetmath|id=|title=}} for copied over text
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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.
47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
- PM: Baker-Campbell-Hausdorff formula(e), id=4321 -- WP guess: Baker-Campbell-Hausdorff formula(e) -- Status:
- PM: closed operator, id=4526 -- WP guess: closed operator -- Status:
- 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: triple scalar product, id=899 -- Duplicate entry.
47A07 Forms (bilinear, sesquilinear, multilinear)
- PM: bilinear form, id=1612 -- Duplicate entry.
- PM: canonical basis for symmetric bilinear forms, id=6631 -- Duplicate entry.
- PM: Hermitian form, id=2468 -- Duplicate entry.
- PM: matrix representation of a bilinear form, id=6630 -- Duplicate entry.
- PM: non-degenerate bilinear form, id=2483 -- Duplicate entry.
- PM: positive definite form, id=2472 -- Duplicate entry.
- PM: symmetric bilinear form, id=2466 -- Duplicate entry.
47A35 Ergodic theory
- PM: ergodic theorem, id=1996 -- Duplicate entry.
47A53 (Semi-) Fredholm operators; index theories
- PM: Fredholm index, id=3863 -- WP guess: Fredholm index -- Status:
- PM: Fredholm module, id=3329 -- Duplicate entry.
- PM: Fredholm operator, id=3353 -- WP guess: Fredholm operator -- Status:
- PM: semi-Fredholm operator, id=5737 -- WP guess: semi-Fredholm operator -- Status:
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:
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:
- PM: self-adjoint operator, id=4527 -- Duplicate entry.
47C05 Operators in algebras
- PM: functional calculus for Hermitian matrices, id=6271 -- WP guess: functional calculus for Hermitian matrices -- Status:
47G30 Pseudodifferential operators
- PM: Dini derivative, id=4714 -- WP: Dini derivative -- Status: Copied. Oleg Alexandrov 3 July 2005 20:08 (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:
47J07 Abstract inverse mapping and implicit function theorems
- PM: Lipschitz inverse mapping theorem, id=5927 -- Duplicate entry.
47L07 Convex sets and cones of operators
- PM: convex hull of S is open if S is open, id=4443 -- Duplicate entry.
- PM: proof that the convex hull of S is open if S is open, id=5587 -- Duplicate entry.
47L25 Operator spaces (= matricially normed spaces)
- PM: operator norm, id=3018 -- WP guess: operator norm -- Status:
47S99 Miscellaneous
- PM: Drazin inverse, id=4738 -- WP guess: Drazin inverse -- Status: