Wikipedia:WikiProject Mathematics/PlanetMath Exchange/46-XX Functional analysis

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

46-XX Functional analysis.

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.
• 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.
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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
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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] 46-00 General reference works (handbooks, dictionaries, bibliographies, etc.)

• PM: T_f is a distribution of zeroth order, id=4434 -- WP: Distribution -- Status:

PM article is a proof which is not included in WP; WP doesn't even define the order of a distribution. Jitse Niesen 13:32, 31 Jan 2005 (UTC)

• PM: \operatorname{p.\!v.}(\frac{1}{x}) is a distribution of first order, id=4473 -- WP: distribution -- Status:

PM article is a proof which is not included in WP; p.v. (1/x) is a nice example of a distribution which should be mentioned in WP. Connection with renormalization? Jitse Niesen 13:32, 31 Jan 2005 (UTC)

• PM: balanced set, id=4425 -- WP guess: balanced set -- Status: NC

No WP article, could perhaps be included in Fréchet space. Jitse Niesen 13:32, 31 Jan 2005 (UTC)

• PM: bounded function, id=4426 -- WP: bounded, bounded function, Banach space -- Status: NM

PM definition is included in bounded, while bounded function uses a different definition coming from order theory. The space of bounded functions is treated as an example in Banach space. Jitse Niesen 13:32, 31 Jan 2005 (UTC)

• PM: bounded set (in a topological vector space), id=4429 -- WP: bounded set, bounded set (topological vector space) -- Status: A

PM definition is more general. Need to create article bounded set, possibly as a redirect to bounded. The thm in PM (compact implies bounded) should be added. Jitse Niesen 13:32, 31 Jan 2005 (UTC)

I recently split the page from bounded set and added the theorem from PM. MathMartin 11:49, 4 May 2005 (UTC)

• PM: Cauchy principal part integral, id=4472 -- WP: Cauchy principal value -- Status: M

Copied the most essential part, as to not disturb too much the existing article. Oleg Alexandrov (talk) 04:52, 10 March 2006 (UTC)

• PM: Cauchy sequence, id=6195 -- WP: Cauchy sequence -- Status: A

Our artilcle is more complete. Paul August ☎ 15:03, Jan 31, 2005 (UTC)

• PM: cone, id=4570 -- WP guess: cone -- Status:

• PM: delta distribution, id=4468 -- WP guess: delta distribution -- Status:

• PM: distribution, id=4427 -- WP guess: distribution -- Status:

• PM: every locally integrable function is a distribution, id=4433 -- WP guess: every locally integrable function is a distribution -- Status:

• PM: function spaces, id=5556 -- WP guess: function spaces -- Status:

• PM: localization for distributions, id=4477 -- WP guess: localization for distributions -- Status:

• PM: locally convex topological vector space, id=4424 -- WP guess: locally convex topological vector space -- Status:

• PM: operations on distributions, id=4440 -- WP guess: operations on distributions -- Status:

• PM: proof of convergence theorem, id=4437 -- WP guess: proof of convergence theorem -- Status:

• PM: sequential characterization of boundedness, id=4525 -- WP guess: sequential characterization of boundedness -- Status:

• PM: smooth distribution, id=4568 -- WP guess: smooth distribution -- Status:

• PM: support of distribution, id=4484 -- WP guess: support of distribution -- Status:

• PM: symmetric set, id=4528 -- WP guess: symmetric set -- Status:

• PM: balanced set, id=7453 -- WP guess: balanced set -- Status:

• PM: boundedness in a topological vector space generalizes boundedness in a metric space, id=7459 -- WP guess: boundedness in a topological vector space generalizes boundedness in a metric space -- Status:

• PM: cone, id=7447 -- WP guess: cone -- Status:

• PM: weak convergence, id=6723 -- WP guess: weak convergence -- Status:

• PM: Hilbert basis, id=8219^new! -- WP guess: Hilbert basis -- Status:

• PM: invariant subspace problem, id=9771^new! -- WP guess: invariant subspace problem -- Status:

• PM: modular mappings in vector spaces over the field of complex numbers, id=8208^new! -- WP guess: modular mappings in vector spaces over the field of complex numbers -- Status:

• PM: modular space, id=8374^new! -- WP guess: modular space -- Status:

[edit] 46A03 General theory of locally convex spaces

• PM: Krein-Milman theorem, id=5921 -- WP: Krein-Milman theorem -- Status: C

Oleg Alexandrov (talk) 19:16, 20 November 2005 (UTC)

• PM: proof of Krein-Milman theorem, id=7251 -- WP guess: proof of Krein-Milman theorem -- Status:

• PM: weak-* topology, id=6855 -- WP guess: weak-* topology -- Status:

• PM: anti-cone, id=9703^new! -- WP guess: anti-cone -- Status:

[edit] 46A08 Barrelled spaces, bornological spaces

• PM: barrel, id=8902^new! -- WP guess: barrel -- Status:

• PM: bornological space, id=8003^new! -- WP guess: bornological space -- Status:

• PM: bounded set, id=8004^new! -- WP guess: bounded set -- Status:

[edit] 46A20 Duality theory

• PM: hyperplane separation, id=9667^new! -- WP guess: hyperplane separation -- Status:

[edit] 46A30 Open mapping and closed graph theorems; completeness (including $B$-, $B r$-completeness)

• PM: closed graph theorem, id=3702 -- WP: closed graph theorem -- Status: A

Oleg Alexandrov (talk) 19:01, 20 November 2005 (UTC)

• PM: open mapping theorem, id=3675 -- WP: open mapping theorem -- Status: A

Oleg Alexandrov (talk) 19:01, 20 November 2005 (UTC)

• PM: proof of closed graph theorem, id=6472 -- WP: proof of closed graph theorem -- Status: N

Oleg Alexandrov (talk) 19:01, 20 November 2005 (UTC)

[edit] 46A40 Ordered topological linear spaces, vector lattices

[edit] 46A55 Convex sets in topological linear spaces; Choquet theory

• PM: convex hull of S is open if S is open, id=4443 -- WP guess: convex hull of S is open if S is open -- Status:

• PM: proof that the convex hull of S is open if S is open, id=5587 -- WP guess: proof that the convex hull of S is open if S is open -- Status:

• PM: conical neighborhood, id=7137 -- WP guess: conical neighborhood -- Status:

[edit] 46A99 Miscellaneous

• PM: Heine-Cantor theorem, id=3066 -- WP: Heine-Cantor theorem -- Status: M

AdamSmithee 15:29, 3 February 2006 (UTC)

• PM: proof of Heine-Cantor theorem, id=4114 -- WP: Heine-Cantor theorem -- Status: N

AdamSmithee 15:29, 3 February 2006 (UTC)

• PM: topological vector space, id=1744 -- WP guess: topological vector space -- Status:

• PM: proof of Heine-Cantor theorem, id=6911 -- WP guess: proof of Heine-Cantor theorem -- Status:

• PM: Riesz representation theorem (of linear functionals on function spaces), id=9857^new! -- WP guess: Riesz representation theorem (of linear functionals on function spaces) -- Status:

[edit] 46Axx Topological linear spaces and related structures

[edit] 46B03 Isomorphic theory (including renorming) of Banach spaces

• PM: hyperbolic isomorphism, id=4315 -- WP guess: hyperbolic isomorphism -- Status:

[edit] 46B04 Isometric theory of Banach spaces

• PM: Mazur-Ulam theorem, id=8524^new! -- WP guess: Mazur-Ulam theorem -- Status:

[edit] 46B07 Local theory of Banach spaces

• PM: Lipschitz inverse mapping theorem, id=5927 -- WP guess: Lipschitz inverse mapping theorem -- Status:

[edit] 46B10 Duality and reflexivity

• PM: Banach-Alaoglu theorem, id=6471 -- WP: Banach-Alaoglu theorem -- Status: A

AdamSmithee 15:38, 3 February 2006 (UTC)

• PM: weak* convergence in normed linear space, id=5229 -- WP guess: weak* convergence in normed linear space -- Status: NC

AdamSmithee 15:38, 3 February 2006 (UTC)

• PM: Proof of Banach-Alaoglu theorem, id=6917 -- WP guess: Proof of Banach-Alaoglu theorem -- Status:

[edit] 46B15 Summability and bases

[edit] 46B20 Geometry and structure of normed linear spaces

• PM: \lim_{p \to \infty} \lVert x \rVert_p = \lVert x \rVert_{\infty}, id=5399 -- WP guess: \lim_p \to \infty \lVert x \rVert_p = \lVert x \rVert_\infty -- Status:

• PM: Banach-Mazur compactum, id=6611 -- WP guess: Banach-Mazur compactum -- Status:

• PM: basic properties of seminorms, id=6240 -- WP guess: basic properties of seminorms -- Status:

• PM: Hahn-Banach theorem, id=3252 -- WP guess: Hahn-Banach theorem -- Status: Status: A

Oleg Alexandrov (talk) 22:58, 10 December 2005 (UTC)

• PM: Minkowski's function, id=6515 -- WP guess: Minkowski's function -- Status: A

Oleg Alexandrov (talk) 05:03, 10 March 2006 (UTC)

• PM: proof of Hahn-Banach theorem, id=4127 -- WP guess: proof of Hahn-Banach theorem -- Status:

• PM: seminorm, id=2322 -- WP guess: seminorm -- Status:

• PM: vector norm, id=91 -- WP guess: vector norm -- Status:

• PM: sub-linear, id=6967 -- WP guess: sub-linear -- Status:

• PM: Golab's theorem, id=9087^new! -- WP guess: Golab's theorem -- Status:

• PM: normed plane, id=9086^new! -- WP guess: normed plane -- Status:

• PM: nuclear space, id=8823^new! -- WP guess: nuclear space -- Status:

• PM: properties of Minkowski's functional, id=7704^new! -- WP guess: properties of Minkowski's functional -- Status:

• PM: vector p-norm, id=92^new! -- WP guess: vector p-norm -- Status:

[edit] 46B25 Classical Banach spaces in the general theory

• PM: proof that L^p spaces are complete, id=6270 -- WP: Lp space -- Status: N

AdamSmithee 15:54, 3 February 2006 (UTC)

[edit] 46B50 Compactness in Banach (or normed) spaces

• PM: proof of Schauder fixed point theorem, id=4457 -- WP guess: proof of Schauder fixed point theorem -- Status:

• PM: Schauder fixed point theorem, id=4455 -- WP guess: Schauder fixed point theorem -- Status:

• PM: Tychonoff fixed point theorem, id=8125^new! -- WP guess: Tychonoff fixed point theorem -- Status:

[edit] 46B99 Miscellaneous

• PM: \ell^p, id=1929 -- WP: Lp space -- Status: A

Oleg Alexandrov (talk) 19:52, 20 November 2005 (UTC)

• PM: all norms on finite-dimensional vector spaces are equivalent, id=5564 -- WP guess: all norms on finite-dimensional vector spaces are equivalent -- Status:

• PM: Banach space, id=1605 -- WP guess: Banach space -- Status:

• PM: Banach-Steinhaus theorem, id=6469 -- WP: Banach-Steinhaus theorem -- Status: A

AdamSmithee 10:25, 6 February 2006 (UTC)

• PM: bounded operator, id=5226 -- WP: bounded operator -- Status: A

Oleg Alexandrov (talk) 06:52, 25 October 2005 (UTC)

• PM: compact operator, id=5966 -- WP: compact operator -- Status: A

Oleg Alexandrov 22:47, 13 September 2005 (UTC)

• PM: continuous linear mapping, id=3741 -- WP: continuous linear mapping and bounded operator -- Status: A

AdamSmithee 10:25, 6 February 2006 (UTC)

• PM: equivalent norms, id=4312 -- WP guess: equivalent norms -- Status:

• PM: every finite dimensional normed vector space is a Banach space, id=6633 -- WP guess: every finite dimensional normed vector space is a Banach space -- Status:

• PM: every subspace of a normed space of finite dimension is closed, id=6632 -- WP guess: every subspace of a normed space of finite dimension is closed -- Status:

• PM: normed vector space, id=1604 -- WP guess: normed vector space -- Status:

• PM: proof of Banach-Steinhaus theorem, id=6470 -- WP: Banach-Steinhaus theorem -- Status: A

AdamSmithee 10:25, 6 February 2006 (UTC)

• PM: all norms are not equivalent, id=7519 -- WP guess: all norms are not equivalent -- Status:

• PM: extended norm, id=6703 -- WP guess: extended norm -- Status:

• PM: scaling of the open ball in a normed vector space, id=7458 -- WP guess: scaling of the open ball in a normed vector space -- Status:

• PM: shift operators in \ell^p, id=7092 -- WP guess: shift operators in \ell^p -- Status:

• PM: approximation property, id=9864^new! -- WP guess: approximation property -- Status:

• PM: necessary and sufficient conditions for a normed vector space to be a Banach space, id=9751^new! -- WP guess: necessary and sufficient conditions for a normed vector space to be a Banach space -- Status:

• PM: quotient norm, id=9749^new! -- WP guess: quotient norm -- Status:

• PM: quotients of Banach spaces by closed subspaces are Banach spaces under the quotient norm, id=9750^new! -- WP guess: quotients of Banach spaces by closed subspaces are Banach spaces under the quotient norm -- Status:

[edit] 46Bxx Normed linear spaces and Banach spaces; Banach lattices

[edit] 46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)

• PM: Bessel inequality, id=3089 -- WP: Bessel inequality -- Status: C

Oleg Alexandrov 02:07, 5 March 2006 (UTC)

• PM: direct integral of Hilbert spaces, id=6364 -- WP guess: direct integral of Hilbert spaces -- Status:

• PM: direct sum of Hilbert spaces, id=6363 -- WP guess: direct sum of Hilbert spaces -- Status:

• PM: Hilbert module, id=3401 -- WP guess: Hilbert module -- Status:

• PM: Hilbert parallelotope, id=6229 -- WP guess: Hilbert parallelotope -- Status:

• PM: Hilbert space, id=1930 -- WP guess: Hilbert space -- Status:

• PM: proof of Bessel inequality, id=3090 -- WP guess: proof of Bessel inequality -- Status:

• PM: Rellich selection theorem, id=6239 -- WP guess: Rellich selection theorem -- Status:

• PM: Riesz sequence, id=5963 -- WP: Riesz sequence -- Status: C

Along with Riesz basis. Ben Cairns 12:55, 18 April 2006 (UTC)

• PM: \vert\langle Tv,v \rangle\vert \leq {\mu} \Vert v \Vert ^2 for all v implies \Vert T \Vert \leq {\mu}, id=7271 -- WP guess: \vert\langle Tv,v \rangle\vert \leq \mu \Vert v \Vert ^2 for all v implies \Vert T \Vert \leq \mu -- Status:

• PM: example of non-separable Hilbert space, id=7691^new! -- WP guess: example of non-separable Hilbert space -- Status:

• PM: generalization of the parallelogram law, id=8227^new! -- WP guess: generalization of the parallelogram law -- Status:

• PM: Hlawka's inequality, id=8228^new! -- WP guess: Hlawka's inequality -- Status:

• PM: parallelogram law, id=8205^new! -- WP guess: parallelogram law -- Status:

• PM: proof of generalization of the parallelogram law, id=8229^new! -- WP guess: proof of generalization of the parallelogram law -- Status:

• PM: proof of parallelogram law, id=8211^new! -- WP guess: proof of parallelogram law -- Status:

• PM: Schur's condition for a matrix to be a bounded operator on l^2, id=7967^new! -- WP guess: Schur's condition for a matrix to be a bounded operator on l^2 -- Status:

• PM: yet another proof of parallelogram law, id=8214^new! -- WP guess: yet another proof of parallelogram law -- Status:

[edit] 46C15 Characterizations of Hilbert spaces

• PM: classification of separable Hilbert spaces, id=1933 -- WP guess: classification of separable Hilbert spaces -- Status:

• PM: proof of classification of separable Hilbert spaces, id=6127 -- WP guess: proof of classification of separable Hilbert spaces -- Status:

• PM: Banach spaces with complemented subspaces, id=8100^new! -- WP guess: Banach spaces with complemented subspaces -- Status:

[edit] 46C99 Miscellaneous

• PM: characterization of tight frames in {\mathbb R}^n, id=5969 -- WP guess: characterization of tight frames in \mathbb R^n -- Status:

• PM: frame, id=5935 -- WP guess: frame -- Status:

• PM: multiresolution analysis, id=5961 -- WP guess: multiresolution analysis -- Status:

• PM: proof of Riesz representation theorem for separable Hilbert spaces, id=6130 -- WP guess: Riesz representation theorem -- Status: N

AdamSmithee 16:13, 3 February 2006 (UTC)

• PM: Riesz representation theorem, id=5585 -- WP: Riesz representation theorem -- Status: A

AdamSmithee 16:13, 3 February 2006 (UTC)

• PM: Riesz-Fischer theorem, id=5586 -- WP guess: Riesz-Fischer theorem -- Status:

• PM: set of sampling, id=5984 -- WP guess: set of sampling -- Status:

• PM: wavelet, id=5959 -- WP guess: wavelet -- Status:

• PM: wavelet set, id=5971 -- WP guess: wavelet set -- Status:

• PM: Gabor frame, id=9448^new! -- WP guess: Gabor frame -- Status:

[edit] 46Cxx Inner product spaces and their generalizations, Hilbert spaces

[edit] 46E15 Banach spaces of continuous, differentiable or analytic functions

• PM: Ascoli-Arzelà theorem, id=2961 -- WP guess: Ascoli-Arzelà theorem -- Status: M

Oleg Alexandrov (talk) 06:57, 25 October 2005 (UTC)

• PM: proof of Ascoli-Arzelà theorem, id=3753 -- WP guess: proof of Ascoli-Arzelà theorem -- Status:

• PM: proof of Stone-Weierstrass theorem, id=6146 -- WP guess: proof of Stone-Weierstrass theorem -- Status:

• PM: Stone-Weierstrass theorem, id=2984 -- WP guess: Stone-Weierstrass theorem -- Status:

[edit] 46E30 Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant

• PM: conjugate index, id=2051 -- WP: conjugate index -- Status: C

Oleg Alexandrov (talk) 04:43, 11 March 2006 (UTC)

• PM: Holder inequality, id=94 -- WP guess: Holder inequality -- Status:

• PM: proof of Holder inequality, id=4110 -- WP guess: proof of Holder inequality -- Status:

• PM: proof of Young Inequality, id=4079 -- WP guess: proof of Young Inequality -- Status:

• PM: Young Inequality, id=4078 -- WP: Young's inequality -- Status: A

Oleg Alexandrov (talk) 04:10, 11 March 2006 (UTC)

• PM: generalization of Young inequality, id=7667^new! -- WP guess: generalization of Young inequality -- Status:

• PM: generalized Hölder inequality, id=9170^new! -- WP guess: generalized Hölder inequality -- Status:

[edit] 46E35 Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems

• PM: Sobolev space, id=6601 -- WP: Sobolev space -- Status: A

Oleg Alexandrov 22:50, 13 September 2005 (UTC)

• PM: weak derivative, id=6600 -- WP: weak derivative -- Status: A

Oleg Alexandrov 22:50, 13 September 2005 (UTC)

• PM: proof of Sobolev inequality for \Omega=\mathbf{R}^n, id=6816 -- WP guess: proof of Sobolev inequality for \Omega=\mathbfR^n -- Status:

• PM: Sobolev inequality, id=6812 -- WP guess: Sobolev inequality -- Status:

[edit] 46E40 Spaces of vector- and operator-valued functions

• PM: vector field, id=902 -- WP guess: vector field -- Status:

[edit] 46Exx Linear function spaces and their duals

[edit] 46F05 Topological linear spaces of test functions, distributions and ultradistributions

• PM: example of Dirac sequence, id=5655 -- WP guess: example of Dirac sequence -- Status:

• PM: space of rapidly decreasing functions, id=4444 -- WP: Schwartz space -- Status: C

linas 21:44, 4 March 2006 (UTC)

[edit] 46F10 Operations with distributions

[edit] 46Fxx Distributions, generalized functions, distribution spaces

[edit] 46G05 Derivatives

• PM: derivative, id=2975 -- WP guess: derivative -- Status:

• PM: higher order derivatives of sine and cosine, id=6395 -- WP guess: higher order derivatives of sine and cosine -- Status:

• PM: Fréchet derivative is unique, id=8221^new! -- WP guess: Fréchet derivative is unique -- Status:

[edit] 46Gxx Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces)

[edit] 46H05 General theory of topological algebras

• PM: Banach algebra, id=3333 -- WP guess: Banach algebra -- Status:

• PM: Hilbert spaces are uniformly convex spaces, id=7021 -- WP guess: Hilbert spaces are uniformly convex spaces -- Status:

• PM: Banach-Krein-mulian theorem, id=7026 -- WP guess: Banach-Krein-Mulian theorem -- Status:

• PM: Hahn-Banach theorem(geometric form), id=7034 -- WP guess: Hahn-Banach theorem (geometric form) -- Status:

• PM: Hyperplane, id=7035 -- WP guess: Hyperplane -- Status:

• PM: proof of Hilbert space is uniformly convex space, id=7167 -- WP guess: proof of Hilbert space is uniformly convex space -- Status:

• PM: Property of uniformly convex Banach Space, id=7011 -- WP guess: Property of uniformly convex Banach Space -- Status:

• PM: Uniformly convex Banach space, id=6983 -- WP guess: Uniformly convex Banach space -- Status:

• PM: uniformly convex space is reflexive, id=7028 -- WP guess: uniformly convex space is reflexive -- Status:

• PM: Gelfand transform, id=9743^new! -- WP guess: Gelfand transform -- Status:

• PM: Gelfand-Mazur theorem, id=9871^new! -- WP guess: Gelfand-Mazur theorem -- Status:

• PM: invertible elements in a Banach algebra form an open set, id=9757^new! -- WP guess: invertible elements in a Banach algebra form an open set -- Status:

• PM: multiplicative linear functional, id=9737^new! -- WP guess: multiplicative linear functional -- Status:

• PM: Neumann series in Banach algebras, id=9756^new! -- WP guess: Neumann series in Banach algebras -- Status:

• PM: normed algebra, id=8286^new! -- WP guess: normed algebra -- Status:

• PM: rotund space, id=8141^new! -- WP guess: rotund space -- Status:

• PM: spectrum is a non-empty compact set, id=9791^new! -- WP guess: spectrum is a non-empty compact set -- Status:

• PM: topological divisor of zero, id=8299^new! -- WP guess: topological divisor of zero -- Status:

• PM: topologically nilpotent, id=8295^new! -- WP guess: topologically nilpotent -- Status:

[edit] 46H15 Representations of topological algebras

• PM: Banach *-algebra representation, id=9843^new! -- WP guess: Banach *-algebra representation -- Status:

[edit] 46H35 Topological algebras of operators

• PM: topological *-algebra, id=6402 -- WP guess: topological *-algebra -- Status:

[edit] 46Hxx Topological algebras, normed rings and algebras, Banach algebras

[edit] 46J10 Banach algebras of continuous functions, function algebras

[edit] 46Jxx Commutative Banach algebras and commutative topological algebras

[edit] 46K05 General theory of topological algebras with involution

[edit] 46K10 Representations of topological algebras with involution

• PM: criterion for a Banach *-algebra representation to be irreducible, id=9845^new! -- WP guess: criterion for a Banach *-algebra representation to be irreducible -- Status:

• PM: representations of Banach *-algebras are continuous, id=9844^new! -- WP guess: representations of Banach *-algebras are continuous -- Status:

[edit] 46Kxx Topological (rings and) algebras with an involution

[edit] 46L05 General theory of $C^*$-algebras

• PM: C^*-algebra, id=3334 -- WP: C*-algebra -- Status: A

Oleg Alexandrov (talk) 23:00, 10 December 2005 (UTC)

• PM: bounded operators on a Hilbert space form a C^*-algebra, id=6438 -- WP: C*-algebra -- Status: A

Our article contains the relevant bit of info. The proof itself which is contained in the PM article, is not wanted. Oleg Alexandrov (talk) 23:02, 10 December 2005 (UTC)

• PM: Gelfand-Naimark representation theorem, id=3335 -- WP guess: Gelfand-Naimark representation theorem -- Status:

• PM: state, id=4574 -- WP guess: state -- Status:

• PM: example of Banach algebra which is not a C^*-algebra for any involution, id=9807^new! -- WP guess: example of Banach algebra which is not a C^*-algebra for any involution -- Status:

• PM: special elements in a C^*-algebra and their spectral properties, id=9862^new! -- WP guess: special elements in a C^*-algebra and their spectral properties -- Status:

• PM: topologically irreducible representations are algebrically irreducible for C^*-algebras, id=9846^new! -- WP guess: topologically irreducible representations are algebrically irreducible for C^*-algebras -- Status:

[edit] 46L10 General theory of von Neumann algebras

• PM: polar decomposition in von Neumann algebras, id=9868^new! -- WP guess: polar decomposition in von Neumann algebras -- Status:

• PM: von Neumann algebra, id=9722^new! -- WP guess: von Neumann algebra -- Status:

• PM: von Neumann algebras contain the range projections of its elements, id=9869^new! -- WP guess: von Neumann algebras contain the range projections of its elements -- Status:

• PM: von Neumann algebras of dimension greater than one contain non-trivial projections, id=9870^new! -- WP guess: von Neumann algebras of dimension greater than one contain non-trivial projections -- Status:

[edit] 46L65 Quantizations, deformations

• PM: Quantization, id=7540 -- WP guess: Quantization -- Status:

• PM: canonical quantization, id=7894^new! -- WP guess: canonical quantization -- Status:

[edit] 46L85 Noncommutative topology

• PM: Gelfand-Naimark theorem, id=4065 -- WP: Gelfand-Naimark theorem -- Status: A

Ours is more elementary and more complete. Oleg Alexandrov (talk) 23:03, 10 December 2005 (UTC)

• PM: Serre-Swan theorem, id=4066 -- WP guess: Serre-Swan theorem -- Status:

[edit] 46L87 Noncommutative differential geometry

• PM: Fredholm module, id=3329 -- WP guess: Fredholm module -- Status:

[edit] 46Lxx Selfadjoint operator algebras ($C^*$-algebras, von Neumann ($W$*-) algebras, etc.)

[edit] 46M05 Tensor products

• PM: triple scalar product, id=899 -- WP guess: triple scalar product -- Status:

[edit] 46Mxx Methods of category theory in functional analysis

[edit] 46N99 Miscellaneous

• PM: Schwarzian derivative, id=9629^new! -- WP guess: Schwarzian derivative -- Status:

[edit] 46Nxx Miscellaneous applications of functional analysis

[edit] 46T12 Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds

• PM: path integral, id=1700 -- WP guess: path integral -- Status:

[edit] 46T20 Continuous and differentiable maps

[edit] 46Txx Nonlinear functional analysis