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Representations of Cuntz algebras associated to quasi-stationary Markov measures

Published online by Cambridge University Press:  30 June 2014

DORIN ERVIN DUTKAY  and
PALLE E. T. JORGENSEN
DORIN ERVIN DUTKAY
Affiliation:
University of Central Florida, Department of Mathematics, 4000 Central Florida Blvd., P.O. Box 161364, Orlando, FL 32816-1364, USA email Dorin.Dutkay@ucf.edu
PALLE E. T. JORGENSEN
Affiliation:
University of Iowa, Department of Mathematics, 14 MacLean Hall, Iowa City, IA 52242-1419, USA email palle-jorgensen@uiowa.edu
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Abstract

In this paper, we answer the question of equivalence, or singularity, of two given quasi-stationary Markov measures on one-sided infinite words, as well as the corresponding question of equivalence of associated Cuntz algebra ${\mathcal{O}}_{N}$-representations. We do this by associating certain monic representations of ${\mathcal{O}}_{N}$ to quasi-stationary Markov measures and then proving that equivalence for a pair of measures is decided by unitary equivalence of the corresponding pair of representations.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 35 , Issue 7 , October 2015 , pp. 2080 - 2093
Copyright
© Cambridge University Press, 2014 

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