The Right Regular Representation of a Compact Right Topological Group
Canadian mathematical bulletin, Tome 41 (1998) no. 4, pp. 463-472
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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.
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
@article{10_4153_CMB_1998_060_2,
author = {Moran, Alan},
title = {The {Right} {Regular} {Representation} of a {Compact} {Right} {Topological} {Group}},
journal = {Canadian mathematical bulletin},
pages = {463--472},
year = {1998},
volume = {41},
number = {4},
doi = {10.4153/CMB-1998-060-2},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1998-060-2/}
}
TY - JOUR AU - Moran, Alan TI - The Right Regular Representation of a Compact Right Topological Group JO - Canadian mathematical bulletin PY - 1998 SP - 463 EP - 472 VL - 41 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1998-060-2/ DO - 10.4153/CMB-1998-060-2 ID - 10_4153_CMB_1998_060_2 ER -
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