A W*-representation, or simply a representation of a von Neumann algebra on a Hilbert space is a morphism of von Neumann algebras , where is the von Neumann algebra of bounded operators on the Hilbert space .
If the map is injective, the resulting notion coincides with that of a “concrete von Neumann algebra”, as opposed to an (abstract) von Neumann algebra. An isomorphism of representations is sometimes referred to as a “spatial isomorphism of concrete von Neumann algebras”.
Such terminology is confusing, but is present in some sources, especially older ones.
The category of W*-representations of is equivalent to the category of Hilbert W*-modules over .
See the article Hilbert W*-module for more information.
Last revised on July 3, 2021 at 17:39:22. See the history of this page for a list of all contributions to it.