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The Right Regular Representation of a Compact Right Topological Group

Published online by Cambridge University Press:  20 November 2018

Alan Moran
Alan Moran*
Affiliation:
School of Mathematics and Statistics Section Pure Mathematics Sheffield University Sheffield S3 7RH England
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Abstract

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We show that for certain compact right topological groups, $\overline{r(G)}$, the strong operator topology closure of the image of the right regular representation of $G$ in $L(H)$, where $H\,=\,{{L}^{2}}\,(G)$, is a compact topological group and introduce a class of representations, $R$ , which effectively transfers the representation theory of $\overline{r(G)}$ over to $G$. Amongst the groups for which this holds is the class of equicontinuous groups which have been studied by Ruppert in [10].We use familiar examples to illustrate these features of the theory and to provide a counter-example. Finally we remark that every equicontinuous group which is at the same time a Borel group is in fact a topological group.

Keywords

22D99
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 41 , Issue 4 , 01 December 1998 , pp. 463 - 472
Copyright
Copyright © Canadian Mathematical Society 1998

References

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