Entropy of a doubly stochastic Markov operator and of its shift on the space of trajectories

Volume 126 / 2012

Paulina Frej Colloquium Mathematicum 126 (2012), 205-216 MSC: Primary 28D20; Secondary 47A35. DOI: 10.4064/cm126-2-5

Abstract

We define the space of trajectories of a doubly stochastic operator on $L^1(X,\mu)$ as a shift space $(X^\mathbb N,\nu,\sigma)$, where $\nu$ is a probability measure defined as in the Ionescu–Tulcea theorem and $\sigma$ is the shift transformation. We study connections between the entropy of a doubly stochastic operator and the entropy of the shift on the space of trajectories of this operator.

Authors

  • Paulina FrejInstitute of Mathematics and Computer Science
    Wrocław University of Technology
    Wybrzeże Wyspiańskiego 27
    50-370 Wrocław, Poland
    e-mail

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