Category:P-Sequence Spaces

This category contains results about $p$-sequence spaces.
Definitions specific to this category can be found in Definitions/P-Sequence Spaces.

Let $p \in \R$ be a real number such that $p \ge 1$.

Let $\BB$ be a Banach space.

The $p$-sequence space (in $\BB$), denoted $\ell^p$ or $\map {\ell^p} \N$, is defined as:

$\ds \ell^p := \set {\sequence {s_n}_{n \mathop \in \N} \in \BB^\N: \sum_{n \mathop = 0}^\infty \norm {s_n}^p < \infty}$

where:

$\BB^\N$ is the set of all sequences in $\BB$

$\norm {s_n}$ denotes the norm of $s_n$.