This is an old revision of the document!
Bounded linear operator
Definition
$X,Y$ … normed vector spaces |
$A\mathcal{BoundedLinOp}(X,Y)$ |
$M\in\mathbb R, M>0$ |
$x\in X$ |
$\exists M.\ \Vert Ax\Vert_Y\le M\Vert x\Vert_X $ |
Discussion
A linear operator on a metrizable vector space is bounded if and only if it is continuous.
Reference
Wikipedia: Bounded linear operator