Download or read book Invariant Means and Finite Representation Theory of $C^*$-Algebras written by Nathanial Patrick Brown and published by American Mathematical Soc.. This book was released on 2006 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.