# Definition:Space of Almost-Zero Sequences

Jump to navigation
Jump to search

## 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.

This article is incomplete.You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by expanding it.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{Stub}}` from the code.If you would welcome a second opinion as to whether your work is correct, add a call to `{{Proofread}}` the page. |

## 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