View source for BK-space

{{Short description|Sequence space that is Banach}}
In [[functional analysis]] and related areas of [[mathematics]], a '''BK-space''' or '''Banach coordinate space''' is a [[sequence space]] endowed with a suitable [[Norm (mathematics)|norm]] to turn it into a [[Banach space]]. All BK-spaces are normable [[FK-space]]s.<ref name="ssmn">{{citation|title=Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral Equations|first1=Jozef|last1=Banas|first2=M.|last2=Mursaleen|publisher=Springer|year=2014|isbn=9788132218869|page=20|url=https://books.google.com/books?id=pWklBAAAQBAJ&pg=PA20}}.</ref>

==Examples==

The [[space of convergent sequences]] <math>c,</math> the [[space of vanishing sequences]] <math>c_0,</math> and the [[space of bounded sequences]] <math>\ell^\infty</math> under the [[supremum norm]] <math>\|\cdot\|_{\infty}.</math><ref name="ssmn"/>

The space of [[absolutely p-summable sequences]] <math>\ell^p</math> with <math>p \geq 1</math> and the norm <math>\|\cdot\|_p.</math><ref name="ssmn"/>

==See also==

* {{annotated link|FK-AK space}}
* {{annotated link|FK-space}}
* {{annotated link|Normed space}}
* {{annotated link|Sequence space}}

==References==

{{reflist}}

{{Banach spaces}}
{{Topological vector spaces}}
{{Functional analysis}}

{{Mathanalysis-stub}}

[[Category:Banach spaces]]
[[Category:Topological vector spaces]]