Markov Operators and $C^{\ast }$-Algebras

Abstract

A Markov operator $P$ acting on $C(X)$, where $X$ is compact, gives rise to a natural topological quiver. We use the theory of such quivers to attach a $C^{\ast }$-algebra to $P$ in a fashion that reflects some of the probabilistic properties of $P$.

Added a few remarks in the second section and a few references. This version will be published in the Houston Journal of Mathematics.

References in corpus (4)

• A construction of $C^{\ast }$-algebras from $C^{\ast }$-correspondences
• KMS States, Entropy and the Variational Principle in full C*-dynamical systems
• Cohomology of topological graphs and Cuntz-Pimsner algebras
• C^*-algebras associated with self-similar sets

Cited by in corpus (3)

• W-Markov measures, transfer operators, wavelets and multiresolutions
• Exel's crossed product and crossed products by completely positive maps
• Topological freeness for $C^{\ast }$-correspondences