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Operator Algebras for Multivariable Dynamics
Kenneth R. Davidson, University of Waterloo, ON, Canada, and Elias G. Katsoulis, East Carolina University, Greenville, NC
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Memoirs of the American Mathematical Society
2011; 53 pp; softcover
Volume: 209
ISBN-10: 0-8218-5302-3
ISBN-13: 978-0-8218-5302-3
List Price: US$60
Individual Members: US$36
Institutional Members: US$48
Order Code: MEMO/209/982
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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

  • Introduction
  • Dilation theory
  • Recovering the dynamics
  • Semisimplicity
  • Open problems and future directions
  • Bibliography
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