In the mathematical field of functional analysis, the space bs consists of all infinite sequences (xi) of real numbers 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 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 via the mapping
Furthermore, the space of convergent sequences c is the image of cs under
See also[edit]
References[edit]
- Dunford, N.; Schwartz, J.T. (1958), Linear operators, Part I, Wiley-Interscience.
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