Difference between revisions of "Bounded"
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* [[Bounded (linear map)]] - Given two [[normed space|normed spaces]], {{M|(X,\Vert\cdot\Vert_X)}} and {{M|(Y,\Vert\cdot\Vert_Y)}} and a [[linear map]] {{M|L:X\rightarrow Y}} we say that ''{{M|L}} is bounded'' if: | * [[Bounded (linear map)]] - Given two [[normed space|normed spaces]], {{M|(X,\Vert\cdot\Vert_X)}} and {{M|(Y,\Vert\cdot\Vert_Y)}} and a [[linear map]] {{M|L:X\rightarrow Y}} we say that ''{{M|L}} is bounded'' if: | ||
** {{M|\exists A>0\ \forall x\in X[\Vert L(x)\Vert_Y\le A\Vert x\Vert_X]}} | ** {{M|\exists A>0\ \forall x\in X[\Vert L(x)\Vert_Y\le A\Vert x\Vert_X]}} | ||
| + | * [[Bounded (ordering)]] | ||
* [[Bounded (sequence)]] | * [[Bounded (sequence)]] | ||
* [[Bounded (set)]] | * [[Bounded (set)]] | ||
| + | ===Related terms=== | ||
| + | * [[Totally bounded (metric space)]] | ||
{{Definition|Topology|Linear Algebra|Functional Analysis|Metric Space}} | {{Definition|Topology|Linear Algebra|Functional Analysis|Metric Space}} | ||
Latest revision as of 19:44, 27 May 2016
Disambiguation
This page lists articles associated with the same title.
If an internal link led you here, you may wish to change the link to point directly to the intended article.
Bounded may refer to:
- Bounded (linear map) - Given two normed spaces, [ilmath](X,\Vert\cdot\Vert_X)[/ilmath] and [ilmath](Y,\Vert\cdot\Vert_Y)[/ilmath] and a linear map [ilmath]L:X\rightarrow Y[/ilmath] we say that [ilmath]L[/ilmath] is bounded if:
- [ilmath]\exists A>0\ \forall x\in X[\Vert L(x)\Vert_Y\le A\Vert x\Vert_X][/ilmath]
- Bounded (ordering)
- Bounded (sequence)
- Bounded (set)
