Franklin

C*-algebras and finite-dimensional approximations / Nathaniel P. Brown, Narutaka Ozawa.

Author/Creator:
Brown, Nathanial P. (Nathanial Patrick), 1972- author.
Publication:
Providence, Rhode Island : American Mathematical Society, [2008]
Series:
Graduate studies in mathematics ; v. 88.
Graduate studies in mathematics, 1065-7339 ; volume 88
Format/Description:
Book
1 online resource (509 p.)
Subjects:
C*-algebras.
Finite groups.
Form/Genre:
Electronic books.
Language:
English
Contents:
""Cover""; ""Title""; ""Copyright""; ""Contents""; ""Preface""; ""Chapter 1. Fundamental Facts""; ""Â1.1. Notation""; ""Â1.2. Subject Index""; ""Â1.3. Von Neumann algebras""; ""Â1.4. Double duals""; ""Â1.5. Completely positive maps""; ""Â1.6. Arveson's Extension Theorem""; ""Â1.7. Voiculescu's Theorem""; ""Part 1. Basic Theory""; ""Chapter 2. Nuclear and Exact C*-Algebras: Definitions, Basic Facts and Examples""; ""Â2.1. Nuclear maps""; ""Â2.2. Nonunital technicalities""; ""Â2.3. Nuclear and exact C*-algebras""; ""Â2.4. First examples""
""Â2.5. C*-algebras associated to discrete groups""""Â2.6. Amenable groups""; ""Â2.7. Type I C*-algebras""; ""Â2.8. References""; ""Chapter 3. Tensor Products""; ""Â3.1. Algebraic tensor products""; ""Â3.2. Analytic preliminaries""; ""Â3.3. The spatial and maximal C*-norms""; ""Â3.4. Takesaki's Theorem""; ""Â3.5. Continuity of tensor product maps""; ""Â3.6. Inclusions and The Trick""; ""Â3.7. Exact sequences""; ""Â3.8. Nuclearity and tensor products""; ""Â3.9. Exactness and tensor products""; ""Â3.10. References""; ""Chapter 4. Constructions""; ""Chapter 4. References""
""Â4.1. Crossed products""""Â4.2. Integer actions""; ""Â4.3. Amenable actions""; ""Â4.4. X xi T-algebras ""; ""Â4.5. Compact group actions and graph C*-algebras ""; ""Â4.6. Cuntz-Pimsner algebras""; ""Â4.7. Reduced amalgamated free products""; ""Â4.8. Maps on reduced amalgamated free products ""; ""Â4.9. References""; ""Chapter 5. Exact Groups and Related Topics""; ""Â5.1. Exact groups ""; ""Â5.2. Groups acting on trees""; ""Â5.3. Hyperbolic groups""; ""Â5.4. Subgroups of Lie groups ""; ""Â5.5. Coarse metric spaces""; ""Â5.6. Groupoids ""; ""Â5.7. References""
""Chapter 6. Amenable Traces and Kirchberg's Factorization Property""""Â6.1. Traces and the right regular representation""; ""Â6.2. Amenable traces""; ""Â6.3. Some motivation and examples""; ""Â6.4. The factorization property and Kazhdan's property (T)""; ""Â6.5.References""; ""Chapter 7. Quasidiagonal C*-Algebras""; ""Â7.1. The definition, easy examples and obstructions""; ""Â7.2. The representation theorem""; ""Â7.3. Homotopy invariance""; ""Â7.4. Two more examples""; ""Â7.5. External approximation""; ""Â7.6. References""; ""Chapter 8. AF Embeddability""
""Â8.1. Stable uniqueness and asymptotically commuting diagrams""""Â8.2. Cones over exact RFD algebras""; ""Â8.3. Cones over general exact algebras""; ""Â8.4. Homotopy invariance""; ""Â8.5. A survey""; ""Â8.6. References""; ""Chapter 9. Local Reflexivity and Other Tensor Product Conditions""; ""Â9.1. Local reflexivity""; ""Â9.2. Tensor product properties""; ""Â9.3. Equivalence of exactness and property C""; ""Â9.4. Corollaries""; ""Â9.5. References""; ""Chapter 10. Summary and Open Problems""; ""Â10.1. Nuclear C*-algebras""; ""Â10.2. Exact C*-algebras""
""Â10.3. Quasidiagonal C*-algebras""
Notes:
Description based upon print version of record.
Includes bibliographical references (pages 493-502) and indexes.
Description based on print version record.
Contributor:
Ozawa, Narutaka, 1974- author.
ISBN:
1-4704-2118-6
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