1550075568-C-Algebras_and_Finite-Dimensional_Approximations__Brown_

C*-Algebras and Finite-Dimensional Approximations ...

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C*-Algebras and Finite-Dimensional Approximations Nathanial P. Brown Narutaka Ozawa Graduate Studies in Mathematics Volume 88 UJ ...

Editorial Board David Cox (Chair) Walter Craig N. V. Ivanov Steven G. Krantz 2000 Mathematics Subject Classification. Primary 46 ...

Contents Preface xi Chapter 1. Fundamental Facts^1 §1.1. Notation 1 §1.2. C* -algebras 2 §1.3. Von Neumann algebras 3 §1.4. Doub ...

vi §3.1. Algebraic tensor products §3.2. Analytic preliminaries §3.3. The spatial and maximal C*-norms §3A. Takesaki's Theorem § ...

Contents Chapter 7. Quasidiagonal C*-Algebras §7.1. The definition, easy examples and obstructions §7.2. The representation theo ...

viii Chapter 12. Approximation Properties for Groups §12.1. Kazhdan's property (T) §12.2. The Haagerup property §12.3. Weak amen ...

Contents §17.4. Topology on Ext §17.5. References Part 4. Appendices ix 439 441 Appendix A. Ultrafilters and Ultraproducts 445 A ...

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Preface This is a book about C -algebras, various types of approximation, and a few of the surprising applications that have bee ...

Xll Preface is the point of operator algebras - it isn't. We simply hope to elevate them from a necessary ally to a revered frie ...

Preface Xlll In Chapter 3 we give a long introduction to the theory of C* -tensor products. Most of the chapter is devoted to de ...

xiv Preface locally reflexive (another important finite-dimensional approximation prop- erty), nuclearity and exactness pass to ...

Preface xv Chapter 15 contains solidity and prime factorization results for certain group von Neumann algebras. The solidity res ...

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Chapter 1 Fundamental Facts We stated in the preface that these notes should be accessible to anyone with a "first course" in op ...

2 1. Fundamental Facts Here Mn(C) is then x n complex matrices and tr is its unique tracial state. A collection of n x n matrice ...

1.3. Von Neumann algebras 3 since limi II (1 - ei)xll is equal to the norm of x +I E A/ I. Putting these .observations together, ...

4 1. Fundamental Facts Definition 1.3.2. The von Neumann algebra M is type II1 if it has no summand of type I and there exists a ...