# Continuous representation

From Encyclopedia of Mathematics

A linear representation of a topological group (semi-group, algebra) in a topological vector space such that the mapping of into defined by the formula , , , is continuous. If is continuous in each argument separately, then in certain cases (for example, when is a locally compact group and is a Banach space) is automatically continuous jointly in the arguments, that is, is a continuous representation.

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#### References

[a1] | G. Warner, "Harmonic analysis on semi-simple Lie groups" , 1 , Springer (1972) |

**How to Cite This Entry:**

Continuous representation.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Continuous_representation&oldid=16881

This article was adapted from an original article by A.I. Shtern (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article