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Invariant Means and Finite Representation Theory of \(C^*\)-Algebras
Nathanial P. Brown, Pennsylvania State University, State College, PA

Memoirs of the American Mathematical Society
2006; 105 pp; softcover
Volume: 184
ISBN-10: 0-8218-3916-0
ISBN-13: 978-0-8218-3916-4
List Price: US$65
Individual Members: US$39
Institutional Members: US$52
Order Code: MEMO/184/865
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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.

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
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