BK-space

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 ${\displaystyle c,}$ the space of vanishing sequences ${\displaystyle c_{0},}$ and the space of bounded sequences ${\displaystyle \ell ^{\infty }}$ under the supremum norm ${\displaystyle \|\cdot \|_{\infty }.}$^[1]

The space of absolutely p-summable sequences ${\displaystyle \ell ^{p}}$ with ${\displaystyle p\geq 1}$ and the norm ${\displaystyle \|\cdot \|_{p}.}$^[1]

See also

• FK-AK space
• FK-space – Sequence space that is Fréchet
• Normed space – Vector space on which a distance is definedPages displaying short descriptions of redirect targets
• Sequence space – Vector space of infinite sequences