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.

Reference

Subset of

Context

Link to graph
Log In
Improvements of the human condition