BK-space
From HandWiki
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 to turn it into a Banach space. All BK-spaces are normable FK-spaces.[1]
Examples
The space of convergent sequences [math]\displaystyle{ c, }[/math] the space of vanishing sequences [math]\displaystyle{ c_0, }[/math] and the space of bounded sequences [math]\displaystyle{ \ell^\infty }[/math] under the supremum norm [math]\displaystyle{ \|\cdot\|_{\infty} }[/math][1]
The space of absolutely p-summable sequences [math]\displaystyle{ \ell^p }[/math] with [math]\displaystyle{ p \geq 1 }[/math] and the norm [math]\displaystyle{ \|\cdot\|_p }[/math][1]
See also
- FK-AK space
- FK-space – Sequence space that is Fréchet
- Sequence space – Vector space of infinite sequences
References
- ↑ 1.0 1.1 1.2 Banas, Jozef; Mursaleen, M. (2014), Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral Equations, Springer, p. 20, ISBN 9788132218869, https://books.google.com/books?id=pWklBAAAQBAJ&pg=PA20.
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