Dictionary

Banach space en · NOUN

Etymology

Named after Polish mathematician Stefan Banach (1892–1945).

Meanings

1. (error-lua-exec, qualifier: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 H¹ and H ᪲, let us make a few elementary observations about the unit ball Σ in the Banach space X.
   • Already in these cases there is convergence in Banach spaces that are not only infinite-dimensional but nonseparable. 1992, R. M. Dudley, M. G. Hahn, James Kuelbs, editors, Probability in Banach Spaces, 8: Proceedings of the Eighth International Conference, Springer, page ix:

Forms

Relateds

Hilbert space

Translations (16)

sh Банацхов про́стор (complete normed vector space) · pl przestrzeń Banacha (complete normed vector space) · ru ба́нахово простра́нство (complete normed vector space) · af Banach-ruimte (complete normed vector space) · da Banachrum (complete normed vector space) · hu Banach-tér (complete normed vector space) · ro spațiu Banach (complete normed vector space) · de Banach-Raum (complete normed vector space) · sh Banachov próstor (complete normed vector space) · it spazio di Banach (complete normed vector space) · ja バナッハ空間 (complete normed vector space) · cmn 巴拿赫空間 /巴拿赫空间 (complete normed vector space) · fr espace de Banach (complete normed vector space) · sv Banachrum (complete normed vector space) · fi Banachin avaruus (complete normed vector space) · bg банахово пространство (complete normed vector space)