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 $$\ell^\infty$$ under the supremum norm $$\|\cdot\|_{\infty}.$$

The space of absolutely p-summable sequences $$\ell^p$$ with $$p \geq 1$$ and the norm $$\|\cdot\|_p.$$