Banach space

== English == === Etymology === Named after Polish mathematician Stefan Banach (1892–1945). === Noun === Banach space (plural Banach spaces) (functional analysis) A normed vector space which is complete with respect to the norm, meaning that Cauchy sequences have well-defined limits that are points in the space. 1962 [Prentice-Hall], Kenneth Hoffman, Banach Spaces of Analytic Functions, 2007, Dover, page 138, Before taking up the extreme points for H 1 {\displaystyle H^{1}} and H ∞ {\displaystyle H^{\infty }} , let us make a few elementary observations about the unit ball Σ {\displaystyle \Sigma } in the Banach space X {\displaystyle X} . ==== Translations ==== === See also === Hilbert space === Further reading === List of Banach spaces on Wikipedia.Wikipedia