Definition:Space of Almost-Zero Sequences
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Definition
The space of almost-zero sequences, denoted $c_{00}$ is defined as:
- $\displaystyle c_{00} := \set{\sequence{z_n}_{n \in \N} \in \C^\N : \exists N \in \R_{> 0}: n > N \implies z_n =0}$
As such, $c_{00}$ is a subspace of $\C^\N$, the space of all complex sequences.
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Also denoted as
The space of almost-zero sequences
- $c_{00}$
can be seen written as:
- $c_c$.
Also see
Sources
- 2017: Amol Sasane: A Friendly Approach to Functional Analysis ... (previous) ... (next): Chapter $1.1$: Normed and Banach spaces. Vector Spaces