Invariant means and finite representation theory of C*-algebras
Abstract
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. II_1-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 II_1-factor representations. This general theory is related to various other problems as well. Applications include: (1) A characterization of R^{\omega}-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.
Cite
@article{arxiv.math/0304009,
title = {Invariant means and finite representation theory of C*-algebras},
author = {Nathanial P. Brown},
journal= {arXiv preprint arXiv:math/0304009},
year = {2007}
}
Comments
This is the final revision! Really. The paper was accepted by Memoirs of AMS, so most of the changes amount to adding details and discussion. 104 pages