Electronic ISBN:  9781470404697 
Product Code:  MEMO/184/865.E 
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 184; 2006; 105 ppMSC: 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.

Table of Contents

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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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