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

1998/04/20 by S. Cavallaro, Cavallaro, S.
Materials Science · Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Lanthanide and Transition Metal Complexes #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.math/9804090

openalex publication_date 1998/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 L²(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.

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