A von Neumann algebra that is commutative.
The category of commutative von Neumann algebras is a full subcategory of the category of von Neumann algebras and has many special properties.
The following five categories are equivalent:
This result can be seen as a measure-theoretic counterpart of the Gelfand duality between commutative unital C*-algebras and compact Hausdorff topological spaces.
Sur certains espaces considérés par M. H. Stone. Summa Brasiliensis Mathematicae 2 (1951), 151–182. PDF.
Equivalences of measure spaces. American Journal of Mathematics 73:2 (1951), 275–313. doi:10.2307/2372178.
Gelfand-type duality for commutative von Neumann algebras. 2005.05284
Last revised on June 1, 2021 at 00:21:40. See the history of this page for a list of all contributions to it.