bounded_linear

Bounded linear operator

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	$\exists M.\ \Vert Av\Vert_W\le M\Vert v\Vert_V$

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