The Criterion of Completely Reducibility for Continuous Representations of Group Algebras

Details The Criterion of Completely Reducibility for Continuous Representations of Group Algebras The Criterion of Completely Reducibility for Continuous Representations of Group Algebras

2010-08-19

arxiv.org/abs/1008.3211v1

Mathematics

Representation Theory

10 pages

Scientific paper

It is shown that every nonsingular continuous representation of the group
algebra $L^{1}(G)$ in Banach spaces is completely reducible if and only if $G$
is a compact group.

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