by Cavallaro, Stefano

Let
$${\mathcal{A}}$$
be an Abelian unital C
^*-algebra and let
$$\hat {\mathcal{A}}$$
denote its Gelfand spectrum. We give some necessary and sufficient conditions for a nondegenerate representation of
$${\mathcal{A}}$$
to be unitarily equivalent to a representation in which the elements of
$${\mathcal{A}}$$
act multiplicatively, by their Gelfand transforms, on a space L
²(
$$\hat {\mathcal{A}}$$
,μ), where μ is a positive measure on the Baire sets of
$$\hat {\mathcal{A}}$$
. We also compare these conditions with the multiplicity-free property of a representation.

DOI: 10.1023/A:1009941513419
Print publication date: 6/1/2000
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