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

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{{Planetmath instructions|topic=47-XX Operator theory}}

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

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=9729 operator topologies], id=9729^{<span style="color:red;">new!</span>} -- WP guess: [[operator topologies]] -- Status:

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

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* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=4524 properties of the adjoint operator], id=4524 -- WP guess: [[properties of the adjoint operator]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=8075 polar decomposition], id=8075^{<span style="color:red;">new!</span>} -- WP guess: [[polar decomposition]] -- Status:

==47A07 Forms (bilinear, sesquilinear, multilinear)==

==47A10 Spectrum, resolvent==

==47A12 Numerical range, numerical radius==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=9212 Dunkl-Williams inequality], id=9212^{<span style="color:red;">new!</span>} -- WP guess: [[Dunkl-Williams inequality]] -- Status:

==47A15 Invariant subspaces==

==47A35 Ergodic theory==

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* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=2092 Euler-Lagrange differential equation (elementary)], id=2092 -- WP guess: [[Euler-Lagrange differential equation (elementary)]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=7457 stationary point], id=7457^{<font color=red>new!</font>} -- WP guess: [[stationary point]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=8074 Russo-Dye theorem], id=8074^{<span style="color:red;">new!</span>} -- WP guess: [[Russo-Dye theorem]] -- Status:

==47Axx General theory of linear operators==

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

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* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=6564 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: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=7654 multiplication operator on L^2], id=7654^{<span style="color:red;">new!</span>} -- WP guess: [[multiplication operator on L^2]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=7798 operator norm of multiplication operator on L^2], id=7798^{<span style="color:red;">new!</span>} -- WP guess: [[operator norm of multiplication operator on L^2]] -- Status:

==47Bxx Special classes of linear operators==

==47C05 Operators in algebras==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=6271 functional calculus for Hermitian matrices], id=6271 -- WP guess: [[functional calculus]] -- Status:

==47C10 Operators in $^*$-algebras==

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=7830 partial isometry], id=7830^{<span style="color:red;">new!</span>} -- WP guess: [[partial isometry]] -- Status:

==47C15 Operators in $C^*$- or von Neumann algebras==

==47Cxx Individual linear operators as elements of algebraic systems==

==47G30 Pseudodifferential operators==

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* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=4714 Dini derivative], id=4714 -- WP: [[Dini derivative]] -- Status: '''C'''

:: [[User:Oleg Alexandrov|Oleg Alexandrov]] 3 July 2005 20:09 (UTC)

==47Gxx Integral, integro-differential, and pseudodifferential operators==

==47H10 Fixed-point theorems==

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* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=3642 proof of Brouwer fixed point theorem], id=3642 -- WP guess: [[proof of Brouwer fixed point theorem]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=8597 KKM lemma], id=8597^{<span style="color:red;">new!</span>} -- WP guess: [[KKM lemma]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=9274 the topologist's sine curve has the fixed point property], id=9274^{<span style="color:red;">new!</span>} -- WP guess: [[the topologist's sine curve has the fixed point property]] -- Status:

==47Hxx Nonlinear operators and their properties==

==47J07 Abstract inverse mapping and implicit function theorems==

==47Jxx Equations and inequalities involving nonlinear operators==

==47L07 Convex sets and cones of operators==

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* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=3018 operator norm], id=3018 -- WP guess: [[operator norm]] -- Status:

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=7091 examples of bounded and unbounded operators], id=7091^{<font color=red>new!</font>} -- WP: [[examples of bounded and unbounded operators]] -- Status: '''A'''

:: [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 04:36, 10 March 2006 (UTC)

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=7732 derivative operator is unbounded in the sup norm], id=7732^{<span style="color:red;">new!</span>} -- WP guess: [[derivative operator is unbounded in the sup norm]] -- Status:

==47Lxx Linear spaces and algebras of operators==

==47S99 Miscellaneous==

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:Just a definition of a rather obscure kind of inverse for operators which are not normally invertible. [[User:Oleg Alexandrov|Oleg Alexandrov]] 20:08, 9 September 2005 (UTC)

* PM: [http://planetmath.org/?op=getobj&amp;from=objects&amp;id=7577 matrix inversion lemma], id=7577^{<font color=red>new!</font>} -- WP guess: [[matrix inversion lemma]] -- Status:

==47Sxx Other (nonclassical) types of operator theory==