Definition:Space of Zero-Limit Sequences

Definition

The space of zero-limit sequences, denoted $c_0$, is defined as:

$\ds c_0 := \set{\sequence{z_n}_{n \in \N} \in \C^\N : \forall \epsilon \in \R_{>0} : \exists N \in \R_{> 0}: n > N \implies \cmod {z_n} < \epsilon}$

As such, $c_0$ is a subspace of $\C^\N$, the space of all complex sequences.

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Also see

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

Sources

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