In the mathematical field of functional analysis, the space bs consists of all infinite sequences (xi) of real numbers or complex numbers is finite. The set of such sequences forms a normed space with the vector space operations defined componentwise

Furthermore, with respect to metric induced by this norm, bs is complete: it is a Banach space.

such that the series is convergent (possibly conditionally) is denoted by cs. This is a closed vector subspace of bs, and so is also a Banach space with the same norm.

The space bs is isometrically isomorphic to the Space of bounded sequences

Furthermore, the space of convergent sequences c is the image of cs

See also

References

• .