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- ...ical analysis]], most spaces which arise in practice turn out to be Banach spaces as well. == Classical Banach spaces == ...2 KB (351 words) - 00:44, 27 July 2024
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- ...ical analysis]], most spaces which arise in practice turn out to be Banach spaces as well. == Classical Banach spaces == ...2 KB (351 words) - 00:44, 27 July 2024
- ==Values in Banach spaces== For a function ''f'' with values in a [[Banach space]] (or [[Fréchet space]]), ''strong measurability'' usually means [[Bo ...1 KB (201 words) - 06:41, 13 May 2024
- ...bbreviation of '''Beck convexity'''. Beck proved the following theorem: A Banach space is ''B''-convex [[if and only if]] every sequence of [[statistical in Let ''X'' be a Banach space with [[norm (mathematics)|norm]] || ||. ''X'' is said to be ''' ...2 KB (296 words) - 17:33, 2 November 2020
- ...urning a subset of the [[product set]] of the members of the family into a Banach space in its own right. The construction is motivated by the classical [[Lp Let <math>(X_i)_{i \in I}</math> be a family of Banach spaces, where <math>I</math> may have arbitrarily large cardinality. Set ...2 KB (385 words) - 06:41, 13 July 2024
- ...Phelps|first2=R. R.|author-link2=Robert R. Phelps|title=A proof that every Banach space is subreflexive|journal=Bulletin of the American Mathematical Society ...<math>B \subseteq X</math> be a bounded, closed, convex subset of a real [[Banach space]] <math>X.</math> Then the set of all [[continuous linear functional] ...2 KB (309 words) - 00:54, 28 December 2023
- ...K-space''' is an [[F-space]] <math>V</math> such that every extension of F-spaces (or twisted sum) of the form ...1</math> are K-spaces,<ref name="kalton"/> as are all finite dimensional [[Banach space]]s. ...1 KB (176 words) - 00:26, 3 November 2022
- ...gical]] [[Hausdorff space]], such that each fiber has the structure of a [[Banach space]]. ...jection]], such that each '''fiber''' <math>B_x := \pi^{-1}(x)</math> is a Banach space. Which satisfies the following conditions: ...2 KB (327 words) - 08:12, 31 May 2022
- ...uced by this norm, ''bs'' is [[Complete metric space|complete]]: it is a [[Banach space]]. ...is a [[Closed set|closed]] [[vector subspace]] of ''bs'', and so is also a Banach space with the same norm. ...2 KB (273 words) - 03:11, 7 February 2025
- {{Short description|Banach space with a compatible structure of a lattice}} ...] and [[order theory]], a '''Banach lattice''' {{math|(''X'',‖·‖)}} is a [[Banach space|complete normed vector space]] with a [[lattice order]], <math>\leq</ ...4 KB (483 words) - 03:33, 27 February 2024
- {{Short description|Mathematical theorem about Banach spaces}} In the [[mathematics|mathematical]] theory of [[Banach space]]s, the '''closed range theorem''' gives necessary and sufficient con ...3 KB (567 words) - 00:46, 20 July 2024
- ..., 1989.</ref> It provides theory for atomic decomposition of a range of [[Banach space]]s of [[distribution (mathematics)|distributions]]. Among others the ...e and therefore it is possible to obtain atomic decompositions for coorbit spaces. ...2 KB (358 words) - 08:18, 23 April 2023
- ...ime}</math> by its [[bidual]]. Said differently, a Grothendieck space is a Banach space for which a [[sequence]] in its dual space converges weak-* if and on Let <math>X</math> be a Banach space. Then the following conditions are equivalent: ...3 KB (486 words) - 02:20, 16 July 2023
- ...ath> to be an operator ideal, it must contain the class of all finite-rank Banach space operators. ...rator acting on a 1-dimensional Banach space, such that for any two Banach spaces <math>X</math> and <math>Y</math> over the same field <math>\mathbb{K}</mat ...3 KB (496 words) - 20:24, 1 November 2019
- ...Lp space|<math>\ell^\infty</math>]], and contains as a closed subspace the Banach space <math>c_0</math> of sequences converging to zero. The [[Dual space|d {{Banach spaces}} ...2 KB (312 words) - 12:46, 12 March 2024
- ...s=Second Series|title=On regularly convex sets in the space conjugate to a Banach space|volume=41|year=1940|issue=3 |jstor=1968735 }}</ref> Let <math>X</math> be a [[Banach space]] and <math>K</math> a weakly compact subset of <math>X</math> (that ...3 KB (361 words) - 16:47, 22 July 2024
- ...], Delta-convergence and weak convergence coincide. For a general class of spaces, similarly to weak convergence, every bounded sequence has a Delta-converge == Characterization in Banach spaces == ...4 KB (547 words) - 20:21, 13 September 2021
- ...short paper by [[Robert C. James]].<ref>James, Robert C. ''A Non-Reflexive Banach Space Isometric With Its Second Conjugate Space.'' Proceedings of the Natio Source:<ref>Morrison, T.J. ''Functional Analysis: An introduction to Banach space theory''. Wiley. (2001)</ref> ...3 KB (387 words) - 05:00, 24 April 2024
- {{Short description|All infinite-dimensional, separable Banach spaces are homeomorphic}} ...r, more generally, [[Fréchet space]]s, are [[homeomorphic]] as topological spaces. The theorem was proved by [[Mikhail Kadets|Mikhail Kadec]] (1966) and [[Ri ...4 KB (661 words) - 01:52, 21 October 2023
- Smith spaces are named after ...type space|stereotype]] and are in the stereotype duality relations with [[Banach space]]s:{{sfn|Akbarov|2003|p=220}}{{sfn|Akbarov|2009|p=467}} ...5 KB (769 words) - 22:26, 7 March 2023
- ...a nonempty [[convex set|convex]] closed bounded set in uniformly convex [[Banach space]] and <math>f</math> is a mapping of <math>K</math> into itself such ...irk]], a new proof of Michael Edelstein showed that, in a uniformly convex Banach space, every iterative sequence <math>f^nx_0</math> of a non-expansive ma ...2 KB (295 words) - 21:32, 23 August 2024