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Results tagged with von-neumann-algebras
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user 61785
Subtag of the [oa.operator-algebras] tag for questions about von Neumann algebras, that is, weak operator topology closed, unital, *-subalgebras of bounded operators on a Hilbert space.
4
votes
Accepted
Topology of state space in von Neumann algebras
Every von Neumann algebra is a C$^*$-algebra. So the usual theorem that a C$^*$-algebra $A$ is (norm) separable iff its state space is first countable in the weak-* topology (i.e. the topology $\sigma …
- 3,768
4
votes
Accepted
About separability of von Neumann algebras
You can find, in any decent textbook on von Neumann algebras, a proof that if $A \subseteq B(\mathcal{H})$ is a von Neumann algebra, and the Hilbert space $\mathcal{H}$ is separable, then the unit bal …
- 3,768
1
vote
Accepted
Explanation of $\sigma$-weak topology von a von Neumann algebra
This is not really research level, and is probably better suited to math.stackexchange, but here's an answer anyway. I will take as given that you know the notation $\sigma(E^*,E)$ for the weak-* topo …
6
votes
About the category of von neumann algebras
I agree with Dmitri Pavlov that separability is not so important in the modern theory of von Neumann algebras, and this answers the second question. However, an example answering the first question ha …
- 3,768