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- ...atics]], particularly in the branch known as [[functional analysis]], a '''Banach space''' is a [[completeness|complete]] [[normed space]]. It is named after famed ...real) Banach space is called its [[dual space]]. This dual space is also a Banach space when endowed with the operator norm on the continuous (hence, bounded) line2 KB (317 words) - 13:13, 14 July 2008
- 137 bytes (15 words) - 13:13, 14 July 2008
- 88 bytes (13 words) - 16:25, 14 July 2008
- 12 bytes (1 word) - 03:27, 18 December 2007
- 423 bytes (60 words) - 15:14, 28 July 2009
Page text matches
- ...atics]], particularly in the branch known as [[functional analysis]], a '''Banach space''' is a [[completeness|complete]] [[normed space]]. It is named after famed ...real) Banach space is called its [[dual space]]. This dual space is also a Banach space when endowed with the operator norm on the continuous (hence, bounded) line2 KB (317 words) - 13:13, 14 July 2008
- {{r|Banach space}}359 bytes (48 words) - 15:04, 28 July 2009
- ...[[topological space|topology]] induced by the operator norm. If ''X'' is a Banach space then its dual space is often denoted by ''X'''. Let ''X'' be a [[Banach space]] over a [[field (mathematics)|field]] ''F'' which is real or complex, then4 KB (605 words) - 17:25, 20 November 2008
- ...t space has additional useful geometric properties that are not found in a Banach space; these properties may be exploited to simplify analysis or to obtain strong [[Banach space]]2 KB (258 words) - 12:33, 4 January 2009
- ...athematics)|norm]]. A [[completeness|complete]] normed space is called a [[Banach space]]. * [[Banach space]]982 bytes (148 words) - 07:17, 3 December 2007
- {{r|Banach space}}297 bytes (43 words) - 12:20, 4 January 2009
- {{r|Banach space}}565 bytes (76 words) - 19:05, 11 January 2010
- {{r|Banach space}}497 bytes (65 words) - 16:06, 11 January 2010
- ...nclude>A set of values {λ} characteristic of an operator ''O'' mapping a [[Banach space]] into itself such that {{nowrap|''O x<sub>λ</sub>''<nowiki> =</nowi282 bytes (45 words) - 11:13, 13 June 2012
- {{r|Banach space}}576 bytes (77 words) - 19:04, 11 January 2010
- {{r|Banach space}}940 bytes (149 words) - 15:13, 28 July 2009
- {{r|Banach space}}1 KB (172 words) - 15:25, 15 May 2011
- {{r|Banach space}}969 bytes (152 words) - 13:42, 25 September 2010
- A bounded, linear operator ''O'' that maps a [[Banach space]] into itself has a '''spectrum''' of values {''λ''} provided there1,021 bytes (155 words) - 11:06, 13 June 2012
- * [[Banach space]]3 KB (441 words) - 12:23, 4 January 2009
- [[Banach space]]s violate the Schröder–Bernstein property;<ref name=Ca>{{harvnb|Casazza6 KB (944 words) - 08:32, 14 October 2013
- [[Banach space]]s violate the Schröder–Bernstein property;<ref name=Ca>{{harvnb|Casazza6 KB (944 words) - 15:09, 23 September 2013
- ..., so that the set of possible values is some functional space, usually a [[Banach space|Banach]] or even [[Hilbert space|Hilbert]] space; the function <math> F </m6 KB (951 words) - 05:01, 8 December 2009
- ...of the metric spaces which appear in other branches of mathematics (e.g. [[Banach space]]s, in particular [[Hilbert space]]s).6 KB (1,068 words) - 07:30, 4 January 2009
- ====[[Normed space|Normed]], [[Banach space|Banach]], [[Inner product space|inner product]], and [[Hilbert space|Hilber ...very normed space is both a linear topological space and a metric space. A Banach space is defined as a complete normed space. Many spaces of sequences or function28 KB (4,311 words) - 08:36, 14 October 2010
- ...rivative]] can be used to define a notion of a holomorphic function on a [[Banach space]] over the field of complex numbers.9 KB (1,434 words) - 15:35, 7 February 2009
- *[[Banach space]]s18 KB (2,669 words) - 08:38, 17 April 2024
- ...ly. Nevertheless it exists, and can be computed numerically. Indeed, the [[Banach space|space]] <math>L_2(\Omega)</math> of all square integrable random variables32 KB (5,149 words) - 15:48, 29 June 2009
- In a general [[Banach space]], these numbers could be (for example) coefficients in a functional expans29 KB (4,366 words) - 09:10, 26 March 2011