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Gelfand-type duality for commutative von Neumann algebras (2005.05284v3)
Published 11 May 2020 in math.OA, math.CT, math.FA, and math.GN
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.