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$C^{*}$-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
Table of Contents
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Front/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