Difference between revisions of "Bounded (linear map)"

Latest revision as of 18:06, 26 February 2016

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-{{Stub page|needs fleshing out}}
+#REDIRECT [[bounded linear map]]
-==Definition==
-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{{rAPIKM}}:
-* {{M|L}} is bounded if (and only if)
-** {{M|\exists A>0\ \forall x\in X\left[\Vert L(x)\Vert_Y\le A\Vert x\Vert_X\right]}}
-==See also==
-* [[Equivalent conditions for a linear map between two normed spaces to be continuous everywhere]] - of which being bounded is an equivalent statement
-==References==
-<references/>
 {{Definition|Linear Algebra|Functional Analysis|Topology|Metric Space}}