Banach space

Banach space
noun Etymology: Stefan Banach died 1945 Polish mathematician Date: 1938 a complete normed vector space

New Collegiate Dictionary. 2001.

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  • Banach space — In mathematics, Banach spaces (pronounced [ˈbanax]) is the name for complete normed vector spaces, one of the central objects of study in functional analysis. A complete normed vector space is a vector space V with a norm ||·|| such that every… …   Wikipedia

  • banach space — noun Usage: usually capitalized B : a normed vector space for which the field of multipliers comprises the real or complex numbers and in which every Cauchy sequence converges to a point in the space * * * /bah nahkh, ban euhk/, Math. a vector… …   Useful english dictionary

  • Banach space — /bah nahkh, ban euhk/, Math. a vector space on which a norm is defined that is complete. [1945 50; after Stefan Banach (1892 1945), Polish mathematician] * * * …   Universalium

  • Banach space — noun A normed vector space which is complete, in the sense that Cauchy sequences converge …   Wiktionary

  • Banach algebra — In mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A over the real or complex numbers which at the same time is also a Banach space. The algebra multiplication and the Banach… …   Wikipedia

  • Banach bundle — In mathematics, a Banach bundle is a vector bundle each of whose fibres is a Banach space, i.e. a complete normed vector space, possibly of infinite dimension.Definition of a Banach bundleLet M be a Banach manifold of class C p with p ≥ 0, called …   Wikipedia

  • Banach manifold — In mathematics, a Banach manifold is a manifold modeled on Banach spaces. Thus it is a topological space in which each point has a neighbourhood homeomorphic to an open set in a Banach space (a more involved and formal definition is given below) …   Wikipedia

  • Banach–Mazur theorem — In mathematics, the Banach–Mazur theorem is a theorem of functional analysis. Very roughly, it states that most well behaved normed spaces are subspaces of the space of continuous paths. It is named after Stefan Banach and Stanisław… …   Wikipedia

  • Space (mathematics) — This article is about mathematical structures called spaces. For space as a geometric concept, see Euclidean space. For all other uses, see space (disambiguation). A hierarchy of mathematical spaces: The inner product induces a norm. The norm… …   Wikipedia

  • Banach–Alaoglu theorem — In functional analysis and related branches of mathematics, the Banach–Alaoglu theorem (also known as Alaoglu s theorem) states that the closed unit ball of the dual space of a normed vector space is compact in the weak* topology. [Rudin, section …   Wikipedia

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