Definition:Space of Almost-Zero Sequences

Definition

The space of almost-zero sequences, denoted $c_{00}$ is defined as:

$c_{00} := \set {\sequence{z_n}_{n \mathop \in \N} \in \C^\N : \exists N \in \R_{>0}: n > N \implies z_n =0}$

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

• Definition:Space of Convergent Sequences
• Definition:Space of Zero-Limit Sequences

Sources

• 2017: Amol Sasane: A Friendly Approach to Functional Analysis ... (previous) ... (next): Chapter $1.1$: Normed and Banach spaces. Vector Spaces