Entropy of a doubly stochastic Markov operator and of its shift on the space of trajectories
Volume 126 / 2012
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.
