Operator Algebras for Multivariable Dynamics

By K. Davidson, Elias G. Katsoulis. 2007

56 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f88b6cff3c5dc38d91a01d03bfc3eb26a95c7866

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Citations in the corpus

Semicrossed Products of Operator Algebras by Semigroups (2014, methodology): “Indeed, such objects have previously been studied in [32, 44, 60].”
Dilation theory, commutant lifting and semicrossed products (2011, background): “The operator algebras of multivariable dynamical systems is developed in [16].”