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 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 ${\ell }^{\mathrm{\infty }}$ under the supremum norm $\Vert \cdot {\Vert }_{\mathrm{\infty }}$

The space of absolutely p-summable sequences ${\ell }^p$ with $p\ge 1$ and the norm $\Vert \cdot {\Vert }_p$

See also

• FK-AK space
• FK-space
• Sequence space – Vector space of infinite sequences