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bounded_linear_operator [2014/03/21 11:11]
127.0.0.1 external edit
bounded_linear_operator [2016/07/31 12:42] (current)
nikolaj
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 ==== Set ==== ==== Set ====
 | @#55CCEE: context ​    | @#55CCEE: $V,W$ ... normed vector spaces | | @#55CCEE: context ​    | @#55CCEE: $V,W$ ... normed vector spaces |
- 
 | @#FFBB00: definiendum | @#FFBB00: $A\in\mathrm{BoundedLinOp}(V,​W)$ | | @#FFBB00: definiendum | @#FFBB00: $A\in\mathrm{BoundedLinOp}(V,​W)$ |
- 
 | @#55EE55: postulate ​  | @#55EE55: $A\in\mathrm{Hom}(V,​W)$ | | @#55EE55: postulate ​  | @#55EE55: $A\in\mathrm{Hom}(V,​W)$ |
- 
 | @#DDDDDD: range       | @#DDDDDD: $M\in\mathbb R, M>0$ | | @#DDDDDD: range       | @#DDDDDD: $M\in\mathbb R, M>0$ |
 | $v\in V$ | | $v\in V$ |
- 
 | @#55EE55: postulate ​  | @#55EE55: $\exists M.\ \Vert Av\Vert_W\le M\Vert v\Vert_V $ | | @#55EE55: postulate ​  | @#55EE55: $\exists M.\ \Vert Av\Vert_W\le M\Vert v\Vert_V $ |
  
-==== Discussion ​====+----- 
 +=== Discussion ===
 A linear operator on a metrizable vector space is bounded if and only if it is continuous. A linear operator on a metrizable vector space is bounded if and only if it is continuous.
 +
 === Reference === === Reference ===
-Wikipedia: [[http://​en.wikipedia.org/​wiki/​Bounded_linear_operator|Bounded linear operator]] +Wikipedia: ​ 
-==== Parents ====+[[http://​en.wikipedia.org/​wiki/​Bounded_linear_operator|Bounded linear operator]] 
 + 
 +-----
 === Subset of === === Subset of ===
 [[Vector space homomorphism]] [[Vector space homomorphism]]
 === Context === === Context ===
 [[Normed vector space]] [[Normed vector space]]
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