A locally compact group $G$ is said to be a Moore group if each irreducible continuous unitary representation of $G$ is finite dimensional.
I'm trying to see why a compact group $G$ would be a Moore group. Any help is appreciated. Thank you.
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1Isn't this just (one form of) the Peter-Weyl theorem? – anomaly Dec 17 '14 at 18:33
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I think you are right. I didn't know about this theorem. – user100478 Dec 17 '14 at 18:38
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@anomaly is there an analogue for Peter-Weyl theorem for semigroups? – user100478 Dec 17 '14 at 19:14
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It doens't hold as stated for semigroups, but there are some results in that direction; I don't know the details. – anomaly Dec 17 '14 at 19:28