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.
|[a1]||G. Warner, "Harmonic analysis on semi-simple Lie groups" , 1 , Springer (1972)|
Continuous representation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Continuous_representation&oldid=16881