Weak ergodicity of nonhomogeneous Markov chains on noncommutative L1-spaces

Mukhamedov, Farrukh (2013) Weak ergodicity of nonhomogeneous Markov chains on noncommutative L1-spaces. Banach Journal of Mathematical Analysis, 7 (2). pp. 53-73. ISSN 1735-8787

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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.

Item Type:	Article (Journal)
Additional Information:	5537/29715
Uncontrolled Keywords:	Dobrushin ergodicity cofficient; weak ergodic; uniform ergodic; L-1-weak ergodic; von Neumann algebra
Subjects:	Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User:	Dr. Farrukh Mukhamedov
Date Deposited:	23 Apr 2013 14:30
Last Modified:	23 Apr 2013 15:06
URI:	http://irep.iium.edu.my/id/eprint/29715

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