Bs space
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In the mathematical field of functional analysis, the space bs consists of all infinite sequences (xi) of real or complex numbers such that
is finite. The set of such sequences forms a normed space with the vector space operations defined componentwise, and the norm given by
Furthermore, with respect to metric induced by this norm, bs is complete: it is a Banach space.
The space of all sequences (xi) 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 ℓ∞ via the mapping
Furthermore, c is the image of cs under T.
[edit] References
- Dunford, N. & Schwartz, J.T. (1958), Linear operators, Part I, Wiley-Interscience.