Tracial invariants, classification and II1 factor representations of Popa algebras
Nathanial P. Brown
Abstract
Using various finite dimensional approximation properties, four convex subsets of the tracial space of a unital C*-algebra are defined. Applications of these tracial invariants include: (1) An analogue of Szego's limit theorem for arbitrary self adjoint operators. (2) A McDuff factor embeds into the ultrapower of the hyperfinite II1 factor if and only if it contains a weakly dense operator system which is injective. (3) There exists a simple, quasidiagonal, real rank zero C*-algebra with non-hyperfinite II1 factor representations and which is not tracially AF. This answers negatively questions of Sorin Popa and, respectively, Huaxin Lin.
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