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.

Examples

• the space of convergent sequences $c$, the space of vanishing sequences $c_{0}$ and the space of bounded sequences $l^{\infty }$ under the supremum norm $\|\cdot \|_{\infty }$
• the space of absolutely p-summable sequences $l^{p}$ with $p\geq 1$ and the norm $\|\cdot \|_{p}$