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C*-algebras and finite-dimensional approximations.


C*-algebras and finite-dimensional approximations.

Brown, Nathanial P. and Narutaka Ozawa.

American Mathematical Society


509 pages



Graduate studies in mathematics; v.88


Built from lectures and other work on approximation theory in the context of operator algebras, this text explains most of the numerous types of approximation properties important to recent and current research and provides proofs of fundamental results only previously available scattered across the literature. After an introduction of fundamental facts (including material on von Neumann algebras and Aarveson's extension theorem), this covers basic theory, such as nuclear and exact C*-algebras, tensor products, constructions, exact groups, amenable traces and Kirchberg's factorization property, quasidiagonal C&-algebras, AF imbeddability, and local reflexivity. Special topics include simple C*-algebras, approximation properties for groups, the weak expectation property and local lifting property, weakly exact von Neumann algebras, and such applications as Herrero's approximation problem and classification of von Neumann algebras.

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Date:Jun 1, 2008
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