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Algebras of operators on Hilbert space, $C^*-$algebras, von Neumann algebras, non-commutative geometry

26 votes
3 answers
2k views

About the category of von neumann algebras

I am looking for one (or more) reference about properties of the category of von Neumann algebra. More precisely, in an answer of a previous question, Dmitri Pavlov mentions that the $W^*$ category …
Oliver's user avatar
  • 357
3 votes
1 answer
331 views

Continuity of a weight on its definition domain in a von Neumann algebra

Let $M$ be a von Neumann algebra and $\varphi$ be a normal weight on it, and let $A$ be its definition subalgebra. We still denote $\varphi$ the extension to $A$ as a linear positive functional. It i …
Oliver's user avatar
  • 357