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.
ISBN: | 9780821839164 |
Publication date: | 30th October 2006 |
Author: | Nathanial P Brown |
Publisher: | American Mathematical Society |
Format: | Paperback |
Pagination: | 105 pages |
Series: | Memoirs of the American Mathematical Society |
Genres: |
Functional analysis and transforms Calculus and mathematical analysis |