Abstract
A definition of an invariant averaging for a linear representation of a group in a locally convex space is given. Main results: A group $H$ is finite if and only if every linear representation of $H$ in a locally convex space has an invariant averaging. A group $H$ is amenable if and only if every almost periodic representation of $H$ in a quasi-complete locally convex space has an invariant averaging. A locally compact group $H$ is compact if and only if every strongly continuous linear representation of $H$ in a quasi-complete locally convex space has an invariant averaging.
Citation
Djavvat Khadjiev. Abdullah Çavuş. "Invariant averagings of locally compact groups." J. Math. Kyoto Univ. 46 (4) 701 - 711, 2006. https://doi.org/10.1215/kjm/1250281600
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