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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
Wikipedia: Bounded linear operator
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