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On the Classification of \(C^*\)-algebras of Real Rank Zero: Inductive Limits of Matrix Algebras over Non-Hausdorff Graphs
Hongbing Su
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Memoirs of the American Mathematical Society
1995; 83 pp; softcover
Volume: 114
ISBN-10: 0-8218-2607-7
ISBN-13: 978-0-8218-2607-2
List Price: US$39
Individual Members: US$23.40
Institutional Members: US$31.20
Order Code: MEMO/114/547
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This work shows that \(K\)-theoretic data is a complete invariant for certain inductive limit \(C^*\)-algebras. \(C^*\)-algebras of this kind are useful in studying group actions. Su gives a \(K\)-theoretic classification of the real rank zero \(C^*\)-algebras that can be expressed as inductive limits of finite direct sums of matrix algebras over finite (possibly non-Hausdorff) graphs or Hausdorff one-dimensional spaces defined as inverse limits of finite graphs. In addition, Su establishes a characterization for an inductive limit of finite direct sums of matrix algebras over finite (possibly non-Hausdorff) graphs to be real rank zero.

Readership

Operator algebraists and functional analysts.

Table of Contents

  • Introduction
  • Small spectrum variation
  • Perturbation
  • Approximate intertwining
  • Asymptotic characterization
  • Existence
  • Uniqueness
  • Classification
  • Applications
  • References
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