Sequence space
Other sequence spaces

The space of bounded series, denote by bs, is the space of sequences x {\displaystyle x} for which

This space, when equipped with the norm

is a Banach space isometrically isomorphic to ℓ ∞, {\displaystyle \ell ^{\infty },} via the linear mapping

The subspace cs consisting of all convergent series is a subspace that goes over to the space c under this isomorphism.

The space Φ or c 00 {\displaystyle c_{00}} is defined to be the space of all infinite sequences with only a finite number of non-zero terms (sequences with finite support). This set is dense in many sequence spaces.
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