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

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

• ChaptersChapter 1. Fundamental factsPart 1. Basic theoryChapter 2. Nuclear and exact $\textrm {C}^*$-algebras: Definitions, basic facts and examplesChapter 3. Tensor productsChapter 4. ConstructionsChapter 5. Exact groups and related topicsChapter 6. Amenable traces and Kirchberg's factorization propertyChapter 7. Quasidiagonal $\textrm {C}^*$-algebrasChapter 8. AF embeddabilityChapter 9. Local reflexivity and other tensor product conditionsChapter 10. Summary and open problemsPart 2. Special topicsChapter 11. Simple $\textrm {C}^*$-algebrasChapter 12. Approximation properties for groupsChapter 13. Weak expectation property and local lifting propertyChapter 14. Weakly exact von Neumann algebrasPart 3. ApplicationsChapter 15. Classification of group von Neumann algebrasChapter 16. Herrero's approximation problemChapter 17. Counterexamples in $\textrm {K}$-homology and $\textrm {K}$-theoryPart 4. AppendicesAppendix A. Ultrafilters and ultraproductsAppendix B. Operator spaces, completely bounded maps and dualityAppendix C. Lifting theoremsAppendix D. Positive definite functions, cocycles and Schoenberg's TheoremAppendix E. Groups and graphsAppendix F. Bimodules over von Neumann algebras

This exciting book takes its readers through a wide palette of topics of current interest within operator algebras and operator space theory. ... These authors have succeeded very well in writing a book that is at the same time a textbook for (graduate) students and a research monograph for experts. ...the entire book makes for enjoyable reading for both types of readers thanks to its clear, informal and witty style. Each section ends with a list of appetizing exercises. ...no other book so far has taken this particular charming path through the landscapes of operator algebras."" - Mathematical Reviews