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Operator Algebras for Multivariable Dynamics
 
Kenneth R. Davidson University of Waterloo, Waterloo, ON, Canada
Elias G. Katsoulis East Carolina University, Greenville, NC
Operator Algebras for Multivariable Dynamics
eBook ISBN:  978-1-4704-0596-0
Product Code:  MEMO/209/982.E
List Price: $63.00
MAA Member Price: $56.70
AMS Member Price: $37.80
Operator Algebras for Multivariable Dynamics
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Operator Algebras for Multivariable Dynamics
Kenneth R. Davidson University of Waterloo, Waterloo, ON, Canada
Elias G. Katsoulis East Carolina University, Greenville, NC
eBook ISBN:  978-1-4704-0596-0
Product Code:  MEMO/209/982.E
List Price: $63.00
MAA Member Price: $56.70
AMS Member Price: $37.80
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2092011; 53 pp
    MSC: Primary 47; Secondary 46; 37;

    Let \(X\) be a locally compact Hausdorff space with \(n\) proper continuous self maps \(\sigma_i:X \to X\) for \(1 \le i \le n\). To this the authors associate two conjugacy operator algebras which emerge as the natural candidates for the universal algebra of the system, the tensor algebra \(\mathcal{A}(X,\tau)\) and the semicrossed product \(\mathrm{C}_0(X)\times_\tau\mathbb{F}_n^+\).

    They develop the necessary dilation theory for both models. In particular, they exhibit an explicit family of boundary representations which determine the C*-envelope of the tensor algebra.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Dilation Theory
    • 3. Recovering the Dynamics
    • 4. Semisimplicity
    • 5. Open Problems and Future Directions
  • 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: 2092011; 53 pp
MSC: Primary 47; Secondary 46; 37;

Let \(X\) be a locally compact Hausdorff space with \(n\) proper continuous self maps \(\sigma_i:X \to X\) for \(1 \le i \le n\). To this the authors associate two conjugacy operator algebras which emerge as the natural candidates for the universal algebra of the system, the tensor algebra \(\mathcal{A}(X,\tau)\) and the semicrossed product \(\mathrm{C}_0(X)\times_\tau\mathbb{F}_n^+\).

They develop the necessary dilation theory for both models. In particular, they exhibit an explicit family of boundary representations which determine the C*-envelope of the tensor algebra.

  • Chapters
  • 1. Introduction
  • 2. Dilation Theory
  • 3. Recovering the Dynamics
  • 4. Semisimplicity
  • 5. Open Problems and Future Directions
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
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