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Lectures on Operator Theory
 
Edited by: B. V. Rajarama Bhat Indian Statistical Institute, Bangalore, India
George A. Elliott University of Toronto, Toronto, ON, Canada
Peter A. Fillmore Dalhousie University, Halifax, NS, Canada
A co-publication of the AMS and Fields Institute
Lectures on Operator Theory
Hardcover ISBN:  978-0-8218-0821-4
Product Code:  FIM/13
List Price: $95.00
MAA Member Price: $85.50
AMS Member Price: $76.00
eBook ISBN:  978-1-4704-3140-2
Product Code:  FIM/13.E
List Price: $89.00
MAA Member Price: $80.10
AMS Member Price: $71.20
Hardcover ISBN:  978-0-8218-0821-4
eBook: ISBN:  978-1-4704-3140-2
Product Code:  FIM/13.B
List Price: $184.00 $139.50
MAA Member Price: $165.60 $125.55
AMS Member Price: $147.20 $111.60
Lectures on Operator Theory
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Lectures on Operator Theory
Edited by: B. V. Rajarama Bhat Indian Statistical Institute, Bangalore, India
George A. Elliott University of Toronto, Toronto, ON, Canada
Peter A. Fillmore Dalhousie University, Halifax, NS, Canada
A co-publication of the AMS and Fields Institute
Hardcover ISBN:  978-0-8218-0821-4
Product Code:  FIM/13
List Price: $95.00
MAA Member Price: $85.50
AMS Member Price: $76.00
eBook ISBN:  978-1-4704-3140-2
Product Code:  FIM/13.E
List Price: $89.00
MAA Member Price: $80.10
AMS Member Price: $71.20
Hardcover ISBN:  978-0-8218-0821-4
eBook ISBN:  978-1-4704-3140-2
Product Code:  FIM/13.B
List Price: $184.00 $139.50
MAA Member Price: $165.60 $125.55
AMS Member Price: $147.20 $111.60
  • Book Details
     
     
    Fields Institute Monographs
    Volume: 132000; 323 pp
    MSC: Primary 46;

    This book resulted from the lectures held at The Fields Institute (Waterloo, ON, Canada). Leading international experts presented current results on the theory of \(C^*\)-algebras and von Neumann algebras, together with recent work on the classification of \(C^*\)-algebras. Much of the material in the book is appearing here for the first time and is not available elsewhere in the literature.

    Titles in this series are co-published with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

    Readership

    Graduate students and research mathematicians interested in operator theory.

  • Table of Contents
     
     
    • 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
  • Additional Material
     
     
  • Reviews
     
     
    • Contains ... a nice illustration of Elliott's classification techniques for inductive limits ... richly illustrated article ... on paths on Coxeter diagrams and sub-factors ... particularly welcome ... Overall this is a very nicely and surprisingly uniformly written book which is of interest both for the novice and the expert in operator algebras ... It may be hoped that the book will inspire some young researcher to new invention.

      CMS Notes
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 132000; 323 pp
MSC: Primary 46;

This book resulted from the lectures held at The Fields Institute (Waterloo, ON, Canada). Leading international experts presented current results on the theory of \(C^*\)-algebras and von Neumann algebras, together with recent work on the classification of \(C^*\)-algebras. Much of the material in the book is appearing here for the first time and is not available elsewhere in the literature.

Titles in this series are co-published with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

Readership

Graduate students and research mathematicians interested in operator theory.

  • 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
  • Contains ... a nice illustration of Elliott's classification techniques for inductive limits ... richly illustrated article ... on paths on Coxeter diagrams and sub-factors ... particularly welcome ... Overall this is a very nicely and surprisingly uniformly written book which is of interest both for the novice and the expert in operator algebras ... It may be hoped that the book will inspire some young researcher to new invention.

    CMS Notes
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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