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 ${\displaystyle l^{\infty }}$ under the supremum norm ${\displaystyle \|\cdot \|_{\infty }}$[1]
• the space of absolutely p-summable sequences ${\displaystyle l^{p}}$ with ${\displaystyle p\geq 1}$ and the norm ${\displaystyle \|\cdot \|_{p}}$[1]

References

1. Banas, Jozef; Mursaleen, M. (2014), Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral Equations, Springer, p. 20, ISBN 9788132218869.