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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

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