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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?

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

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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Topology of state space in von Neumann algebras

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