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 vanishing 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

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

Functional analysis (topics – glossary)

Spaces

Banach Besov Fréchet Hilbert Hölder Nuclear Orlicz Schwartz Sobolev topological vector
Properties	barrelled complete dual (algebraic/topological) locally convex reflexive separable

Theorems

Operators

Algebras

Open problems

Applications

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