BK-space

Template:Short description 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

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