Invariant means and finite representation theory of C*-algebras
Brown, Nathanial P.
Original · EN
Various subsets of the tracial state space of a unital C*-algebra are studied. The largest of these subsets has a natural interpretation as the space of invariant means. II₁-factor representations of a class of C*-algebras considered by Sorin Popa are also studied. These algebras are shown to have an unexpected variety of II₁-factor representations. This general theory is related to various other problems as well. Applications include: (1) A characterization of Rω-embeddable factors in terms of Lance's WEP. (2) A classification theorem for certain simple, nuclear C*-algebras with unique trace. (3) For a self-adjoint operator there always exists a filtration such that the finite section method (from numerical analysis) works as well as could be hoped for. (4) New examples of non-tracially AF algebras which answer negatively questions of Sorin Popa and Huaxin Lin.
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