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

References

1 2 3 Banas, Jozef; Mursaleen, M. (2014), Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral Equations, Springer, p. 20, ISBN 9788132218869 .

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