## Bounded linear operator

### Set

 context $V,W$ … normed vector spaces definiendum $A\in\mathrm{BoundedLinOp}(V,W)$ postulate $A\in\mathrm{Hom}(V,W)$ range $M\in\mathbb R, M>0$ $v\in V$ postulate $\exists M.\ \Vert Av\Vert_W\le M\Vert v\Vert_V$

#### Discussion

A linear operator on a metrizable vector space is bounded if and only if it is continuous.