Memoirs of the American Mathematical Society 2006; 105 pp; softcover Volume: 184 ISBN10: 0821839160 ISBN13: 9780821839164 List Price: US$65 Individual Members: US$39 Institutional Members: US$52 Order Code: MEMO/184/865
 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 in operator algebras. Table of Contents  Introduction
 Notation, definitions and useful facts
 Amenable traces and stronger approximation properties
 Examples and special cases
 Finite representations
 Applications and connections with other areas
 Bibliography
