Hypocontinuous bilinear map - Wikipedia
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In mathematics, a hypocontinuous is a condition on bilinear maps of topological vector spaces that is weaker than continuity but stronger than separate continuity. Many important bilinear maps that are not continuous are, in fact, hypocontinuous.
If ,
and
are topological vector spaces then a bilinear map
is called hypocontinuous if the following two conditions hold:
Sufficient conditions
[edit]
Theorem:[1] Let X and Y be barreled spaces and let Z be a locally convex space. Then every separately continuous bilinear map of into Z is hypocontinuous.
- Bilinear map – Function of two vectors linear in each argument
- Dual system
- ^ a b Trèves 2006, pp. 424–426.
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