Multiplicity-free representations of commutative C*-algebras and spectral properties
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.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.