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arXiv · 2005.05284

Gelfand-type duality for commutative von Neumann algebras

Dmitri Pavlov
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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.

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BibTeXRIS

Dmitri Pavlov. 2020-05-11. Gelfand-type duality for commutative von Neumann algebras. https://doi.org/10.1016/j.jpaa.2021.106884

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