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1. • CommentRowNumber1.
   • CommentAuthorDmitri Pavlov
   • CommentTimeApr 14th 2021
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexCreated with this content: ## Definition A __W\*-representation__, or simply a __representation__ of a [[von Neumann algebra]] $A$ on a [[Hilbert space]] $H$ is a morphism of [[von Neumann algebras]] $A\to B(H)$, where $B(H)$ is the [[von Neumann algebra]] of [[bounded operators]] on the [[Hilbert space]] $H$. ## Properties The category of [[W*-representations]] of $A$ is equivalent to the category of [[Hilbert W*-modules]] over $A$. See the article [[Hilbert W*-module]] for more information. ## Related concepts * [[Hilbert W*-module]] * [[von Neumann algebra]] * [[duality between geometry and algebra]] [[!redirects W*-representations]] <a href="https://ncatlab.org/nlab/revision/W%2A-representation/1">v1</a>, <a href="https://ncatlab.org/nlab/show/W%2A-representation">current</a>

   Created with this content:

   Definition

   A W*-representation, or simply a representation of a von Neumann algebra $A$ on a Hilbert space $H$ is a morphism of von Neumann algebras $A\to B(H)$, where $B(H)$ is the von Neumann algebra of bounded operators on the Hilbert space $H$.

   Properties

   The category of W*-representations of $A$ is equivalent to the category of Hilbert W*-modules over $A$.

   See the article Hilbert W*-module for more information.

   Related concepts

   • Hilbert W*-module

   • von Neumann algebra

   • duality between geometry and algebra

   !redirects W*-representations

   v1, current