Abstract
In this paper we study certain properties of Dobrushin's ergod- icity coe�cient for stochastic operators de�ned 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 coe�cient. We provide a su�cient condi- tions for such processes to satisfy the weak ergodicity. Moreover, a necessary and su�cient 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.
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