Abstract view
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The right regular representation of a compact right topological group
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Published:1998-12-01
Printed: Dec 1998
Abstract
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
${\cal L}({\cal H})$, where ${\cal H} = \L2$, is a compact
topological group and introduce a class of representations,
${\cal R}$, 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.
