Invariant Means and Finite Representation Theory of C*-Algebras

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. In addition to developing some general theory we also show that these ideas are related to numerous other problems inoperator algebras.Brown, Nathanial P. is the author of 'Invariant Means and Finite Representation Theory of C*-Algebras ', published 2006 under ISBN 9780821839164 and ISBN 0821839160.