nLab
commutative von Neumann algebra

Idea

A von Neumann algebra that is commutative.

Properties

The category of commutative von Neumann algebras is a full subcategory of the category of von Neumann algebras and has many special properties.

Duality

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.

References

Last revised on June 1, 2021 at 00:21:40. See the history of this page for a list of all contributions to it.