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.

Definition

If , and are topological vector spaces then a bilinear map is called hypocontinuous if the following two conditions hold:

Sufficient conditions

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.

Examples

See also

References

  1. ^ a b Trèves 2006, pp. 424-426.

Bibliography