Open centralizers and the continuity of group representations

Schochet, Claude; Schreiber, Bertram

doi:10.1090/S0002-9939-1981-0603609-3

Open centralizers and the continuity of group representations
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by Claude Schochet and Bertram Schreiber

Proc. Amer. Math. Soc. 82 (1981), 99-104

DOI: https://doi.org/10.1090/S0002-9939-1981-0603609-3

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Abstract:

Let $G$ be a locally compact group, $\pi :G \to \mathfrak {L}({L^2}(G))$ the right regular representation of $G$, and ${G^c} = \{ x \in G:$: the function $g \rightsquigarrow \pi (gx{g^{ - 1}})$ is norm continuous}. This note is devoted to the study of ${G^c}$. In particular, the compactly generated groups for which $G = {G^c}$ are characterized.

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