# Invariant Means and Finite Representation Theory of \(C^{*}\)-Algebras

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*Nathanial P. Brown*

#### Table of Contents

# Table of Contents

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

- Contents vii8 free
- Chapter 1. Introduction 110 free
- Chapter 2. Notation, definitions and useful facts 918 free
- Chapter 3. Amenable traces and stronger approximation properties 1524
- Chapter 4. Examples and special cases 3544
- Chapter 5. Finite representations 5564
- Chapter 6. Applications and connections with other areas 6776
- 6.1. Elliott's classification program 6776
- 6.2. Counterexamples to questions of Lin and Popa 7786
- 6.3. Connes' embedding problem 8291
- 6.4. Amenable traces and numerical analysis 8796
- 6.5. Amenable traces and obstructions in K-homology 92101
- 6.6. Stable finiteness versus quasidiagonality 97106
- 6.7. Questions 100109

- Bibliography 103112