**Memoirs of the American Mathematical Society**

2011;
53 pp;
Softcover

MSC: Primary 47;
Secondary 46; 37

Print ISBN: 978-0-8218-5302-3

Product Code: MEMO/209/982

List Price: $63.00

AMS Member Price: $37.80

MAA member Price: $56.70

**Electronic ISBN: 978-1-4704-0596-0
Product Code: MEMO/209/982.E**

List Price: $63.00

AMS Member Price: $37.80

MAA member Price: $56.70

# Operator Algebras for Multivariable Dynamics

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*Kenneth R. Davidson; Elias G. Katsoulis*

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.