Banach space

English Etymology en Stefan Banach = Polish mathematician 1892 1945. Noun en 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 and , let us make a few elementary observations about the unit ball in the Banach space . en 1992 R. M. Dudley; M. G. Hahn; James Kuelbs Probability in Banach Spaces, 8: Proceedings of the Eighth International Conference https://books.google.com.au/books?id=_qGsljjxgsUC&pg=PR9&dq=%22Banach+space%22%7C%22Banach+spaces%22&hl=en&sa=X&ved=0ahUKEwick96fwOjWAhVHVLwKHZ7zAJQQ6AEI6QMwTg#v=onepage&q=%22Banach%20space%22%7C%22Banach%20spaces%22&f=false ix Springer Already in these cases there is convergence in Banach spaces that are not only infinite-dimensional but nonseparable. en 2013 R. E. Showalter Monotone Operators in Banach Space and Nonlinear Partial Differential Equations American Mathematical Society https://books.google.com.au/books?id=xDoJRZHEH2IC&pg=PA35&dq=%22Banach+space%22%7C%22Banach+spaces%22&hl=en&sa=X&ved=0ahUKEwick96fwOjWAhVHVLwKHZ7zAJQQ6AEIhAMwPA#v=onepage&q=%22Banach%20space%22%7C%22Banach%20spaces%22&f=false 35 [A] Banach space is a complete normed linear space . Its dual space is the linear space of all continuous linear functionals , and it has norm ; is also a Banach space. Translations complete normed vector space Afrikaans: af Banach-ruimte Bulgarian: bg банахово пространство n Chinese: Mandarin: cmn 巴拿赫空間 Bānáhè kōngjiān Danish: da Banachrum n Finnish: fi Banachin avaruus French: fr espace de Banach m German: de Banach-Raum m Hungarian: hu Banach-tér Italian: it spazio di Banach ? Japanese: ja バナッハ空間 Banahha-kūkan Polish: pl przestrzeń Banacha f Romanian: ro spațiu Banach n Russian: ru ба́нахово простра́нство n Serbo-Croatian: Cyrillic: sh Банацхов про́стор m Latin: sh Banachov próstor m Swedish: sv Banachrum n See also en Hilbert space Further reading List of Banach spaces en Functional analysis