Category:P-Norms

This category contains results about $p$-norms.

Let $p \ge 1$ be a real number.

Let $\ell^p$ denote the $p$-sequence space.

Let $\mathbf x = \sequence {x_n} \in \ell^p$.

Then the $p$-norm of $\mathbf x$ is defined as:

$\ds \norm {\mathbf x}_p = \paren {\sum_{n \mathop = 0}^\infty \size {x_n}^p}^{1/p}$