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bounded_linear_operator [2013/09/13 21:51]
nikolaj
bounded_linear_operator [2016/07/31 12:42]
nikolaj
Line 1: Line 1:
 ===== Bounded linear operator ===== ===== Bounded linear operator =====
-==== Definition ​==== +==== Set ==== 
-| @#88DDEE: $V,W$ ... normed vector spaces | +| @#55CCEE: context ​    | @#55CCEE: $V,W$ ... normed vector spaces | 
- +| @#FFBB00: definiendum ​| @#FFBB00: $A\in\mathrm{BoundedLinOp}(V,​W)$ | 
-| @#FFBB00: $A\in\mathrm{BoundedLinOp}(V,​W)$ | +| @#55EE55: postulate ​  | @#55EE55: $A\in\mathrm{Hom}(V,​W)$ | 
- +| @#DDDDDD: range       | @#DDDDDD: $M\in\mathbb R, M>0$ |
-| @#55EE55: $A\in\mathrm{Hom}(V,​W)$ | +
- +
-| @#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: $\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.
  
-==== Discussion ==== 
-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]]
-=== Requirements ​===+=== Context ​===
 [[Normed vector space]] [[Normed vector space]]
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