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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.
Definition source: English Wiktionary via Wiktextract
Usage: error-lua-exec
Qualifier: functional analysis
Examples
- 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.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
Named after Polish mathematician Stefan Banach (1892–1945).
Across languages
Translations
15 source translations are retained for this English entry.
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Afrikaans:
Banach-ruimte
— complete normed vector space
-
Bulgarian:
банахово пространство
(banahovo prostranstvo)
— complete normed vector space
-
Chinese Mandarin:
巴拿赫空間 /巴拿赫空间
(Bānáhè kōngjiān)
— complete normed vector space
-
Danish:
Banachrum
— complete normed vector space
-
French:
espace de Banach
— complete normed vector space
-
German:
Banach-Raum
— complete normed vector space
-
Hungarian:
Banach-tér
— complete normed vector space
-
Italian:
spazio di Banach
— complete normed vector space
-
Japanese:
バナッハ空間
(Banahha-kūkan)
— complete normed vector space
-
Polish:
przestrzeń Banacha
— complete normed vector space
-
Romanian:
spațiu Banach
— complete normed vector space
-
Russian:
ба́нахово простра́нство
(bánaxovo prostránstvo)
— complete normed vector space
-
Serbo-Croatian:
Банацхов про́стор
— complete normed vector space
-
Serbo-Croatian:
Banachov próstor
— complete normed vector space
-
Swedish:
Banachrum
— complete normed vector space
