Continuous representation
From Encyclopedia of Mathematics
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.
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.
Comments
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
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