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Open centralizers and the continuity of group representations


Authors: Claude Schochet and Bertram Schreiber
Journal: Proc. Amer. Math. Soc. 82 (1981), 99-104
MSC: Primary 22D05
DOI: https://doi.org/10.1090/S0002-9939-1981-0603609-3
MathSciNet review: 603609
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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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DOI: https://doi.org/10.1090/S0002-9939-1981-0603609-3
Article copyright: © Copyright 1981 American Mathematical Society

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