Multiplicity-free representations of commutative C*-algebras and spectral properties

S. Cavallaro

Multiplicity-free representations of commutative C*-algebras and spectral properties

Operator Algebras 2012-01-20 v3

Authors: S. Cavallaro

Abstract

Let A be a commutative unital C*-algebra and let S denote its Gelfand spectrum. We give some necessary and sufficient conditions for a nondegenerate representation of A to be unitarily equivalent to a multiplicative representation on a space L^2(S, m), where m is a positive measure on the Baire sets of S. We also compare these conditions with the multiplicity-free property of a representation.

Keywords

commutative c*-algebras multiplicity-free representations gelfand spectrum unitary equivalence spectral properties

Cite

@article{arxiv.math/9804090,
  title  = {Multiplicity-free representations of commutative C*-algebras and spectral properties},
  author = {S. Cavallaro},
  journal= {arXiv preprint arXiv:math/9804090},
  year   = {2012}
}

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