Tracial invariants, classification and II_1 factor representations of Popa algebras

Details Tracial invariants, classification and II_1 factor representations of Popa algebras Tracial invariants, classification and II_1 factor representations of Popa algebras

2001-11-27

arxiv.org/abs/math/0111286v3

Mathematics

Operator Algebras

LaTeX 2e, 37 pages, minor revisions and (hopefully) improved exposition

Scientific paper

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 II_1 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 II_1 factor representations and which is not tracially AF. This answers negatively questions of Sorin Popa and, respectively, Huaxin Lin.

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