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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.

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Topology of state space in von Neumann algebras

What are the sufficient conditions for a von Neumann algebra to have a first countable set of states with respect to the weak * operator topology?
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