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C*-algebras and finite-dimensional approximations

Author: Nathanial P Brown; Narutaka Ozawa
Publisher: Providence, R.I. : American Mathematical Society, ©2008.
Series: Graduate studies in mathematics, v. 88.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
"C*-approximation theory has provided the foundation for many of the most important conceptual breakthroughs and applications of operator algebras. This book 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, insofar as that is  Read more...
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Nathanial P Brown; Narutaka Ozawa
ISBN: 9780821843819 0821843818
OCLC Number: 180190949
Description: xv, 509 pages : illustrations ; 26 cm.
Contents: Fundamental facts --
Nuclear and exact 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 --
Simple C* -algebras --
Approximation properties for groups --
Weak expectation property and local lifting property --
Weakly exact von Neumann algebras --
Classification of group von Neumann algebras --
Herrero's approximation problem --
Counterexamples in K- homology and K- theory --
Appendices: A. Ultrafilters and ultraproducts --
B. Operator spaces, completely bounded maps and duality --
C. Lifting theorems --
D. Positive definite functions, cocycles and Schoenberg's theorem --
E. Groups and graphs --
F. Bimodules over von Neumann algebras. Nuclear and exact 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 production conditions --
Simple C*-algebras --
Approximation properties for groups --
Weak expectation property and local lifting property --
Weakly exact von Neumann algebras --
Classification of group von Neumann algebras --
Herrero's approximation problem --
Counterexamples in k-homology and k-theory --
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.
Series Title: Graduate studies in mathematics, v. 88.
Responsibility: Nathaniel P. Brown, Narutaka Ozawa.

Abstract:

$\textrm{C}^*$-approxmation theory has provided the foundation for many of the most important conceptual breakthroughs and applications of operator algebras. This book systematically studies (most  Read more...

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