Gelfand-type duality for commutative von Neumann algebras

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Abstract

We show that the following five categories are equivalent: (1) the opposite category of commutative von Neumann algebras; (2) compact strictly localizable enhanced measurable spaces; (3) measurable locales; (4) hyperstonean locales; (5) hyperstonean spaces. This result can be seen as a measure-theoretic counterpart of the Gelfand duality between commutative unital C-algebras and compact Hausdorff topological spaces. This paper is also available as arXiv:2005.05284v3.

Original languageEnglish
Article number106884
JournalJournal of Pure and Applied Algebra
Volume226
Issue number4
DOIs
StatePublished - Apr 2022

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