===== Bounded linear operator =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $V,W$ ... normed vector spaces |
| @#FFBB00: definiendum | @#FFBB00: $A\in\mathrm{BoundedLinOp}(V,W)$ |
| @#55EE55: postulate   | @#55EE55: $A\in\mathrm{Hom}(V,W)$ |
| @#DDDDDD: range       | @#DDDDDD: $M\in\mathbb R, M>0$ |
| $v\in V$ |
| @#55EE55: postulate   | @#55EE55: $\exists M.\ \Vert Av\Vert_W\le M\Vert v\Vert_V $ |

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

=== Reference ===
Wikipedia: 
[[http://en.wikipedia.org/wiki/Bounded_linear_operator|Bounded linear operator]]

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=== Subset of ===
[[Vector space homomorphism]]
=== Context ===
[[Normed vector space]]