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Viser: C*-Algebras and Finite-Dimensional Approximations
C*-Algebras and Finite-Dimensional Approximations
(2008)
Sprog: Engelsk
American Mathematical Society
1.499,00 kr.
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Detaljer om varen
- Hardback: 509 sider
- Udgiver: American Mathematical Society (Marts 2008)
- ISBN: 9780821843819
This text systematically studies most of the numerous types of approximation properties that have been important in recent years - nuclearity, exactness, quasidiagonality, local reflexivity, and others. Moreover, it contains user-friendly proofs of many fundamental results that were previously hard to extract from the literature.
Fundamental facts; Basic theory: Nuclear and exact $\textrm{C}^*$-algebras: Definitions, basic facts and examples; Tensor products; Constructions; Exact groups and related topics; Amenable traces and Kirchberg's factorization property; Quasidiagonal C*-algebras; AF embeddability; Local reflexivity and other tensor product conditions; Summary and open problems; Special topics: Simple $\textrm{C}^*$-algebras; Approximation properties for groups; Weak expectation property and local lifting property; Weakly exact von Neumann algebras; Applications: Classification of group von Neumann algebras; Herrero's approximation problem; Counterexamples in $\textrm{K}$-homology and $\textrm{K}$-theory; Appendices: Ultrafilters and ultraproducts; Operator spaces, completely bounded maps and duality; Lifting theorems; Positive definite functions, cocycles and Schoenberg's Theorem; Groups and graphs; Bimodules over von Neumann algebras; Bibliography; Notation index; Subject
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