AMS eBook CollectionsOne of the world's most respected mathematical collections, available in digital format for your library or institution

$C^{*}$-Algebras and Finite-Dimensional Approximations

About this Title

Nathanial P. Brown, Pennsylvania State University, State College, PA and Narutaka Ozawa, University of California, Los Angeles, Los Angeles, CA

Publication: Graduate Studies in Mathematics
Publication Year: 2008; Volume 88
ISBNs: 978-0-8218-4381-9 (print); 978-1-4704-2118-2 (online)
DOI: https://doi.org/10.1090/gsm/088
MathSciNet review: MR2391387
MSC: Primary 46L05; Secondary 43A07, 46-02, 46L10

View full volume as PDF

Read more about this volume

Table of Contents

Download chapters as PDF

Front/Back Matter

• View this volume's front and back matter

Chapters

• Chapter 1. Fundamental facts

Part 1. Basic theory

• Chapter 2. Nuclear and exact $\textrm {C}^*$-algebras: Definitions, basic facts and examples
• Chapter 3. Tensor products
• Chapter 4. Constructions
• Chapter 5. Exact groups and related topics
• Chapter 6. Amenable traces and Kirchberg’s factorization property
• Chapter 7. Quasidiagonal $\textrm {C}^*$-algebras
• Chapter 8. AF embeddability
• Chapter 9. Local reflexivity and other tensor product conditions
• Chapter 10. Summary and open problems

Part 2. Special topics

• Chapter 11. Simple $\textrm {C}^*$-algebras
• Chapter 12. Approximation properties for groups
• Chapter 13. Weak expectation property and local lifting property
• Chapter 14. Weakly exact von Neumann algebras

Part 3. Applications

• Chapter 15. Classification of group von Neumann algebras
• Chapter 16. Herrero’s approximation problem
• Chapter 17. Counterexamples in $\textrm {K}$-homology and $\textrm {K}$-theory

Part 4. Appendices

• Appendix A. Ultrafilters and ultraproducts
• Appendix B. Operator spaces, completely bounded maps and duality
• Appendix C. Lifting theorems
• Appendix D. Positive definite functions, cocycles and Schoenberg’s Theorem
• Appendix E. Groups and graphs
• Appendix F. Bimodules over von Neumann algebras