# Gelfand-type duality for commutative von Neumann algebras

@article{Pavlov2020GelfandtypeDF, title={Gelfand-type duality for commutative von Neumann algebras}, author={Dmitri Pavlov}, journal={arXiv: Operator Algebras}, year={2020} }

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.

#### 5 Citations

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