Geodesic
The Right Regular Representation of a Compact Right Topological Group
Canadian mathematical bulletin, Tome 41 (1998) no. 4, pp. 463-472

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-1998-060-2
Mots-clés : 22D99 
Moran, Alan. The Right Regular Representation of a Compact Right Topological Group. Canadian mathematical bulletin, Tome 41 (1998) no. 4, pp. 463-472. doi: 10.4153/CMB-1998-060-2
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