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Lectures on Operator Theory

About this Title

B. V. Rajarama Bhat, Indian Statistical Institute, Bangalore, India, George A. Elliott, University of Toronto, Toronto, ON, Canada and Peter A. Fillmore, Dalhousie University, Halifax, NS, Canada, Editors

Publication: Fields Institute Monographs
Publication Year: 2000; Volume 13
ISBNs: 978-0-8218-0821-4 (print); 978-1-4704-3140-2 (online)
DOI: https://doi.org/10.1090/fim/013
MathSciNet review: MR1743202
MSC: Primary 46Lxx; Secondary 46-01, 46-02

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Table of Contents

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Front/Back Matter

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Part 1. C*-algebras

• Chapter 1. C*-algebras: Definitions and examples
• Chapter 2. C*-algebras: Constructions
• Chapter 3. Positivity in C*-algebras
• Chapter 4. K-theory I
• Chapter 5. Tensor products of C*-algebras
• Chapter 6. Crossed products I
• Chapter 7. Crossed products II: Examples
• Chapter 8. Free products
• Chapter 9. K-theory II: Roots in topology and index theory
• Chapter 10. C*-algebraic K-theory made concrete, or trick or treat with $2 \times 2$ matrix algebras
• Chapter 11. Dilation theory
• Chapter 12. C*-algebras and mathematical physics
• Chapter 13. C*-algebras and several complex variables

Part 2. Von Neumann algebras

• Chapter 14. Basic structure of von Neumann algebras
• Chapter 15. von Neumann algebras (Type $II_1$ factors)
• Chapter 16. The equivalence between injectivity and hyperfiniteness, part I
• Chapter 17. The equivalence between injectivity and hyperfiniteness, part II
• Chapter 18. On the Jones index
• Chapter 19. Introductory topics on subfactors
• Chapter 20. The Tomita-Takesaki theory explained
• Chapter 21. Free products of von Neumann algebras
• Chapter 22. Semigroups of endomorphisms of $\mathcal {B}(H)$

Part 3. Classification of C*-algebras

• Chapter 23. AF-algebras and Bratteli diagrams
• Chapter 24. Classification of amenable C*-algebras I
• Chapter 25. Classification of amenable C*-algebras II
• Chapter 26. Simple AI-algebras and the range of the invariant
• Chapter 27. Classification of simple purely infinite C*-algebras I

Part 4. Hereditary subalgebras of certain simple non real rank zero C*-algebras

• Chapter 28. Introduction
• Chapter 29. The isomorphism theorem
• Chapter 30. The range of the invariant
• Chapter 31. Bibliography

Paths on Coxeter diagrams: From platonic solids and singularities to minimal models and subfactors

• Chapter 32. The Kauffman-Lins recoupling theory
• Chapter 33. Graphs and connections
• Chapter 34. An extension of the recoupling model
• Chapter 35. Relations to minimal models and subfactors