Von Neumann Algebras
In a related context, an approximately finite dimensional, or hyperfinite, von Neumann algebra is one with a separable predual and contains a weakly dense AF C*-algebra. Murray and von Neumann showed that, up to isomorphism, there exists a unique hyperfinite type II1 factor. Connes obtained the analogous result for the II∞ factor. Powers exhibited a family of non-isomorphic type III hyperfinite factors with cardinality of the continuum. Today we have a complete classification of hyperfinite factors.
Read more about this topic: Approximately Finite Dimensional C*-algebra
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