l2 Space

Definition

${\ell }^2=\left\{x:\mathbb{N}\to \mathbb{R}|\sum _{i=1}^{\infty }{x}_i^2<\infty \right\}$ ${\ell }^2$ space consists of all infinite real sequences $x=(x_1,x_2,\dots ,x_n,\dots )$ such that $\sum _{i=1}^{\infty }{x}_i^2<\infty$.