The Dobrushin ergodicity coefficient and the ergodicity of noncommutative Markov chains

Abstract

In this paper, we study the notion of the Dobrushin ergodicity coefficient for positive contractions defined on the predual M* of von Neumann algebra M. Moreover, in terms of this coefficient, we prove ergodic-type theorems for nonhomogeneous Markov chains on M*. © 2013 Elsevier Ltd.