eBook ISBN:  9781470405960 
Product Code:  MEMO/209/982.E 
List Price:  $63.00 
MAA Member Price:  $56.70 
AMS Member Price:  $37.80 
eBook ISBN:  9781470405960 
Product Code:  MEMO/209/982.E 
List Price:  $63.00 
MAA Member Price:  $56.70 
AMS Member Price:  $37.80 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 209; 2011; 53 ppMSC: 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


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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.

Chapters

1. Introduction

2. Dilation Theory

3. Recovering the Dynamics

4. Semisimplicity

5. Open Problems and Future Directions