Operator Algebras for Multivariable Dynamics (Memoirs of the American Mathematical Society) - Softcover

Davidson, Kenneth R.; Katsoulis, Elias G.

Softcover

ISBN 10: 0821853023 ISBN 13: 9780821853023

Publisher: American Mathematical Society, 2011

Synopsis

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.|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.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2011
• Language: English
• ISBN 10: 0821853023
• ISBN 13: 9780821853023
• Binding: Paperback
• Number of pages: 53