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.
- ISBN13 9780821839164
- Publish Date 1 November 2006
- Publish Status Active
- Publish Country US
- Imprint American Mathematical Society
- Format Paperback
- Pages 105
- Language English