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Invariant Means and Finite Representation Theory of $C^*$-Algebras

Nathanial P. Brown Pennsylvania State University, State College, PA
Available Formats:
Electronic ISBN: 978-1-4704-0469-7
Product Code: MEMO/184/865.E
List Price: $65.00 MAA Member Price:$58.50
AMS Member Price: $39.00 Click above image for expanded view Invariant Means and Finite Representation Theory of$C^*$-Algebras Nathanial P. Brown Pennsylvania State University, State College, PA Available Formats:  Electronic ISBN: 978-1-4704-0469-7 Product Code: MEMO/184/865.E  List Price:$65.00 MAA Member Price: $58.50 AMS Member Price:$39.00
• Book Details

Memoirs of the American Mathematical Society
Volume: 1842006; 105 pp
MSC: Primary 46;

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.

• Chapters
• 1. Introduction
• 2. Notation, definitions and useful facts
• 3. Amenable traces and stronger approximation properties
• 4. Examples and special cases
• 5. Finite representations
• 6. Applications and connections with other areas
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Volume: 1842006; 105 pp
MSC: Primary 46;

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.

• Chapters
• 1. Introduction
• 2. Notation, definitions and useful facts
• 3. Amenable traces and stronger approximation properties
• 4. Examples and special cases
• 5. Finite representations
• 6. Applications and connections with other areas
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