Weak ergodicity of nonhomogeneous Markov chains on noncommutative L1-spaces - Mukhamedov, Farrukh (Ferdowsi University of Mashhad., 2013)
In this paper we study certain properties of Dobrushin's ergod- icity coecient for stochastic operators dened on noncommutative L 1 -spaces associated with semi-nite von Neumann algebras. Such results extends the well-known classical ones to a noncommutative setting. This allows us to in- vestigate the weak ergodicity of nonhomogeneous discrete Markov processes (NDMP) by means of the ergodicity coecient. We provide a sucient condi- tions for such processes to satisfy the weak ergodicity. Moreover, a necessary and sucient condition is given for the satisfaction of the L 1 -weak ergodicity of NDMP. It is also provided an example showing that L 1 -weak ergodicity is weaker that weak ergodicity. We applied the main results to several concrete examples of noncommutative NDMP.