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{{Planetmath instructions|topic=47-XX Operator theory}}
 
==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 guess: [[Baker-Campbell-Hausdorff formula(e)]] -- Status:
 
* PM: [http://planetmath.org/?op=getobj&from=objects&id=4526 closed operator], id=4526 -- WP guess: [[closed operator]] -- Status:
 
* PM: [http://planetmath.org/?op=getobj&from=objects&id=4523 densely defined], id=4523 -- WP guess: [[densely defined]] -- Status:
 
* 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=899 triple scalar product], id=899 -- '''Duplicate entry'''.
:See [[Wikipedia:WikiProject Mathematics/PlanetMath Exchange/46-XX Functional analysis#46M05 Tensor products|46M05 Tensor products]]
 
==47A07 Forms (bilinear, sesquilinear, multilinear)==
* PM: [http://planetmath.org/?op=getobj&from=objects&id=1612 bilinear form], id=1612 -- '''Duplicate entry'''.
:See [[Wikipedia:WikiProject Mathematics/PlanetMath Exchange/11-XX Number theory#11E39 Bilinear and Hermitian forms|11E39 Bilinear and Hermitian forms]]
 
* PM: [http://planetmath.org/?op=getobj&from=objects&id=6631 canonical basis for symmetric bilinear forms], id=6631 -- '''Duplicate entry'''.
:See [[Wikipedia:WikiProject Mathematics/PlanetMath Exchange/11-XX Number theory#11E39 Bilinear and Hermitian forms|11E39 Bilinear and Hermitian forms]]
 
* PM: [http://planetmath.org/?op=getobj&from=objects&id=2468 Hermitian form], id=2468 -- '''Duplicate entry'''.
:See [[Wikipedia:WikiProject Mathematics/PlanetMath Exchange/11-XX Number theory#11E39 Bilinear and Hermitian forms|11E39 Bilinear and Hermitian forms]]
 
* PM: [http://planetmath.org/?op=getobj&from=objects&id=6630 matrix representation of a bilinear form], id=6630 -- '''Duplicate entry'''.
:See [[Wikipedia:WikiProject Mathematics/PlanetMath Exchange/11-XX Number theory#11E39 Bilinear and Hermitian forms|11E39 Bilinear and Hermitian forms]]
 
* PM: [http://planetmath.org/?op=getobj&from=objects&id=2483 non-degenerate bilinear form], id=2483 -- '''Duplicate entry'''.
:See [[Wikipedia:WikiProject Mathematics/PlanetMath Exchange/11-XX Number theory#11E39 Bilinear and Hermitian forms|11E39 Bilinear and Hermitian forms]]
 
* PM: [http://planetmath.org/?op=getobj&from=objects&id=2472 positive definite form], id=2472 -- '''Duplicate entry'''.
:See [[Wikipedia:WikiProject Mathematics/PlanetMath Exchange/11-XX Number theory#11E39 Bilinear and Hermitian forms|11E39 Bilinear and Hermitian forms]]
 
* PM: [http://planetmath.org/?op=getobj&from=objects&id=2466 symmetric bilinear form], id=2466 -- '''Duplicate entry'''.
:See [[Wikipedia:WikiProject Mathematics/PlanetMath Exchange/11-XX Number theory#11E39 Bilinear and Hermitian forms|11E39 Bilinear and Hermitian forms]]
 
==47A35 Ergodic theory==
* PM: [http://planetmath.org/?op=getobj&from=objects&id=1996 ergodic theorem], id=1996 -- '''Duplicate entry'''.
:See [[Wikipedia:WikiProject Mathematics/PlanetMath Exchange/37-XX Dynamical systems and ergodic theory#37A30 Ergodic theorems, spectral theory, Markov operators|37A30 Ergodic theorems, spectral theory, Markov operators]]
 
==47A53 (Semi-) Fredholm operators; index theories==
* PM: [http://planetmath.org/?op=getobj&from=objects&id=3863 Fredholm index], id=3863 -- WP guess: [[Fredholm index]] -- Status:
 
* PM: [http://planetmath.org/?op=getobj&from=objects&id=33293353 Fredholm moduleoperator], id=33293353 -- '''DuplicateWP guess: [[Fredholm operator]] -- Status: entry'''.
:See [[Wikipedia:WikiProject Mathematics/PlanetMath Exchange/46-XX Functional analysis#46L87 Noncommutative differential geometry|46L87 Noncommutative differential geometry]]
 
* PM: [http://planetmath.org/?op=getobj&from=objects&id=33535737 semi-Fredholm operator], id=33535737 -- WP guess: [[semi-Fredholm operator]] -- Status:
 
* PM: [http://planetmath.org/?op=getobj&from=objects&id=5737 semi-Fredholm operator], id=5737 -- WP guess: [[semi-Fredholm operator]] -- Status:
 
==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:
 
* PM: [http://planetmath.org/?op=getobj&from=objects&id=1995 calculus of variations], id=1995 -- WP guess: [[calculus of variations]] -- Status:
 
* PM: [http://planetmath.org/?op=getobj&from=objects&id=6393 derivation of Euler-Lagrange differential equation (advanced)], id=6393 -- WP guess: [[derivation of Euler-Lagrange differential equation (advanced)]] -- Status:
 
* PM: [http://planetmath.org/?op=getobj&from=objects&id=6401 derivation of Euler-Lagrange differential equation (elementary)], id=6401 -- WP guess: [[derivation of Euler-Lagrange differential equation (elementary)]] -- Status:
 
* PM: [http://planetmath.org/?op=getobj&from=objects&id=6400 Euler-Lagrange differential equation (advanced)], id=6400 -- WP guess: [[Euler-Lagrange differential equation (advanced)]] -- Status:
 
* 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:
 
==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:
 
* PM: [http://planetmath.org/?op=getobj&from=objects&id=4527 self-adjoint operator], id=4527 -- '''Duplicate entry'''.
:See [[Wikipedia:WikiProject Mathematics/PlanetMath Exchange/47-XX Operator theory#47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.)|47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.)]]
 
==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 for Hermitian matrices]] -- Status:
 
==47G30 Pseudodifferential operators==
* PM: [http://planetmath.org/?op=getobj&from=objects&id=4714 Dini derivative], id=4714 -- WP: [[Dini derivative]] -- Status: '''CopiedC'''.
:: [[User:Oleg Alexandrov|Oleg Alexandrov]] 3 July 2005 20:09 (UTC)
 
==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:
 
* PM: [http://planetmath.org/?op=getobj&from=objects&id=4480 Brouwer fixed point in one dimension], id=4480 -- WP guess: [[Brouwer fixed point in one dimension]] -- Status:
 
* PM: [http://planetmath.org/?op=getobj&from=objects&id=3046 Brouwer fixed point theorem], id=3046 -- WP guess: [[Brouwer fixed point theorem]] -- Status:
 
* PM: [http://planetmath.org/?op=getobj&from=objects&id=4704 fixed point property], id=4704 -- WP guess: [[fixed point property]] -- Status:
 
* 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:
 
==47J07 Abstract inverse mapping and implicit function theorems==
* PM: [http://planetmath.org/?op=getobj&from=objects&id=5927 Lipschitz inverse mapping theorem], id=5927 -- '''Duplicate entry'''.
:See [[Wikipedia:WikiProject Mathematics/PlanetMath Exchange/46-XX Functional analysis#46B07 Local theory of Banach spaces|46B07 Local theory of Banach spaces]]
 
==47L07 Convex sets and cones of operators==
* PM: [http://planetmath.org/?op=getobj&from=objects&id=4443 convex hull of S is open if S is open], id=4443 -- '''Duplicate entry'''.
:See [[Wikipedia:WikiProject Mathematics/PlanetMath Exchange/46-XX Functional analysis#46A55 Convex sets in topological linear spaces; Choquet theory|46A55 Convex sets in topological linear spaces; Choquet theory]]
 
* PM: [http://planetmath.org/?op=getobj&from=objects&id=5587 proof that the convex hull of S is open if S is open], id=5587 -- '''Duplicate entry'''.
:See [[Wikipedia:WikiProject Mathematics/PlanetMath Exchange/46-XX Functional analysis#46A55 Convex sets in topological linear spaces; Choquet theory|46A55 Convex sets in topological linear spaces; Choquet theory]]
 
==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:
 
==47S99 Miscellaneous==
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