Invariant Means and Finite Representation Theory of C-algebras
نویسندگان
چکیده
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 R-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. Dedicated to my big, beautiful family.
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