**Memoirs of the American Mathematical Society**

1995;
83 pp;
Softcover

MSC: Primary 46;

Print ISBN: 978-0-8218-2607-2

Product Code: MEMO/114/547

List Price: $41.00

AMS Member Price: $24.60

MAA Member Price: $36.90

**Electronic ISBN: 978-1-4704-0126-9
Product Code: MEMO/114/547.E**

List Price: $41.00

AMS Member Price: $24.60

MAA Member Price: $36.90

# On the Classification of \(C^{*}\)-algebras of Real Rank Zero: Inductive Limits of Matrix Algebras over Non-Hausdorff Graphs

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*Hongbing Su*

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

# Table of Contents

## On the Classification of $C^{*}$-algebras of Real Rank Zero: Inductive Limits of Matrix Algebras over Non-Hausdorff Graphs

- CONTENTS v6 free
- CHAPTER 1 Introduction 110 free
- CHAPTER 2 Small spectrum variation 413 free
- CHAPTER 3 Perturbation 918
- CHAPTER 4 Approximate intertwining 2736
- CHAPTER 5 Asymptotic characterization 2938
- CHAPTER 6 Existence 3746
- CHAPTER 7 Uniqueness 5160
- CHAPTER 8 Classification 6776
- CHAPTER 9 Applications 7382
- REFERENCES 8291