Definition:P-Sequence Space

Definition
Let $p \in \R$, $p \ge 1$.

The $p$-sequence space, denoted $\ell^p$, is defined as:


 * $\ell^p := \left\{{\left({z_n}\right)_{n \in \N} \in \C^\N: \displaystyle \sum_{n \mathop = 1}^\infty \left\vert{z_n}\right\vert^p < \infty}\right\}$

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

Also known as
Some authors call sequence spaces Lebesgue spaces, but this term is reserved for a more general object on ProofWiki.

Also see

 * Lebesgue Space
 * Sequence Space is Lebesgue Space