Gelfand-type duality for commutative von Neumann algebras
Operator Algebras
2021-09-10 v3 Category Theory
Functional Analysis
General Topology
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.
Cite
@article{arxiv.2005.05284,
title = {Gelfand-type duality for commutative von Neumann algebras},
author = {Dmitri Pavlov},
journal= {arXiv preprint arXiv:2005.05284},
year = {2021}
}
Comments
47 pages. Comments and questions are very welcome. v2: Added Theorem 1.2, Proposition 4.59, Remark 5.12. v3: Identical to the journal version except for formatting and style