\begin{definition}[Definition:P-Sequence Space]
Let $p \in \R$, $p \ge 1$.
The '''$p$-sequence space''', denoted $\ell^p$ or $\map {\ell^p} \N$, is defined as:
:$\ds \ell^p := \set {\sequence {z_n}_{n \mathop \in \N} \in \C^\N: \sum_{n \mathop = 0}^\infty \size {z_n}^p < \infty}$
As such, $\ell^p$ is a subspace of $\C^\N$, the space of all complex sequences.
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\end{definition}