Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
Share this page via the icons above, or by copying the link below:
Copy To Clipboard
Successfully Copied!
Gromov-Hausdorff Distance for Quantum Metric Spaces/Matrix Algebras Converge to the Sphere for Quantum Gromov-Hausdorff Distance
 
Marc A. Rieffel University of California, Berkeley, CA
Gromov-Hausdorff Distance for Quantum Metric Spaces/Matrix Algebras Converge to the Sphere for Quantum Gromov-Hausdorff Distance
eBook ISBN:  978-1-4704-0394-2
Product Code:  MEMO/168/796.E
List Price: $63.00
MAA Member Price: $56.70
AMS Member Price: $37.80
Gromov-Hausdorff Distance for Quantum Metric Spaces/Matrix Algebras Converge to the Sphere for Quantum Gromov-Hausdorff Distance
Click above image for expanded view
Gromov-Hausdorff Distance for Quantum Metric Spaces/Matrix Algebras Converge to the Sphere for Quantum Gromov-Hausdorff Distance
Marc A. Rieffel University of California, Berkeley, CA
eBook ISBN:  978-1-4704-0394-2
Product Code:  MEMO/168/796.E
List Price: $63.00
MAA Member Price: $56.70
AMS Member Price: $37.80
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1682004; 91 pp
    MSC: Primary 46; Secondary 53; 58; 60

    By a quantum metric space we mean a \(C^*\)-algebra (or more generally an order-unit space) equipped with a generalization of the usual Lipschitz seminorm on functions which one associates to an ordinary metric. We develop for compact quantum metric spaces a version of Gromov–Hausdorff distance. We show that the basic theorems of the classical theory have natural quantum analogues. Our main example involves the quantum tori, \(A_\theta\). We show, for consistently defined “metrics”, that if a sequence \(\{\theta_n\}\) of parameters converges to a parameter \(\theta\), then the sequence \(\{A_{\theta_n}\}\) of quantum tori converges in quantum Gromov–Hausdorff distance to \(A_\theta\).

    Readership

    Graduate students and research mathematicians interested in functional analysis.

  • Table of Contents
     
     
    • Chapters
    • Gromov-Hausdorff distance for quantum metric spaces
    • 1. Introduction
    • 2. Compact quantum metric spaces
    • 3. Quotients (= “subsets”)
    • 4. Quantum Gromov-Hausdorff distance
    • 5. Bridges
    • 6. Isometries
    • 7. Distance zero
    • 8. Actions of compact groups
    • 9. Quantum tori
    • 10. Continuous fields of order-unit spaces
    • 11. Continuous fields of lip-norms
    • 12. Completeness
    • 13. Finite approximation and compactness
    • Matrix algebras converge to the sphere for quantum Gromov-Hausdorff distance
    • 0. Introduction
    • 1. The quantum metric spaces
    • 2. Choosing the bridge constant $\gamma $
    • 3. Compact semisimple Lie groups
    • 4. Covariant symbols
    • 5. Contravariant symbols
    • 6. Conclusion of the proof of Theorem 3.2
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1682004; 91 pp
MSC: Primary 46; Secondary 53; 58; 60

By a quantum metric space we mean a \(C^*\)-algebra (or more generally an order-unit space) equipped with a generalization of the usual Lipschitz seminorm on functions which one associates to an ordinary metric. We develop for compact quantum metric spaces a version of Gromov–Hausdorff distance. We show that the basic theorems of the classical theory have natural quantum analogues. Our main example involves the quantum tori, \(A_\theta\). We show, for consistently defined “metrics”, that if a sequence \(\{\theta_n\}\) of parameters converges to a parameter \(\theta\), then the sequence \(\{A_{\theta_n}\}\) of quantum tori converges in quantum Gromov–Hausdorff distance to \(A_\theta\).

Readership

Graduate students and research mathematicians interested in functional analysis.

  • Chapters
  • Gromov-Hausdorff distance for quantum metric spaces
  • 1. Introduction
  • 2. Compact quantum metric spaces
  • 3. Quotients (= “subsets”)
  • 4. Quantum Gromov-Hausdorff distance
  • 5. Bridges
  • 6. Isometries
  • 7. Distance zero
  • 8. Actions of compact groups
  • 9. Quantum tori
  • 10. Continuous fields of order-unit spaces
  • 11. Continuous fields of lip-norms
  • 12. Completeness
  • 13. Finite approximation and compactness
  • Matrix algebras converge to the sphere for quantum Gromov-Hausdorff distance
  • 0. Introduction
  • 1. The quantum metric spaces
  • 2. Choosing the bridge constant $\gamma $
  • 3. Compact semisimple Lie groups
  • 4. Covariant symbols
  • 5. Contravariant symbols
  • 6. Conclusion of the proof of Theorem 3.2
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.