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}
}
  • D. Pavlov
  • Published 11 May 2020
  • Mathematics
  • arXiv: Operator Algebras
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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