Weak ergodicity of nonhomogeneous markov chains on noncommutative l1-spaces

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10 Citations (Scopus)


Abstract. In this paper we study certain properties of Dobrushin’s ergodicity coefficient for stochastic operators defined on noncommutative L1-spaces associated with semi-finite von Neumann algebras. Such results extends the well-known classical ones to a noncommutative setting. This allows us to investigate the weak ergodicity of nonhomogeneous discrete Markov processes (NDMP) by means of the ergodicity coefficient. We provide a sufficient conditions for such processes to satisfy the weak ergodicity. Moreover, a necessary and sufficient condition is given for the satisfaction of the L1-weak ergodicity of NDMP. It is also provided an example showing that L1-weak ergodicity is weaker that weak ergodicity. We applied the main results to several concrete examples of noncommutative NDMP.

Original languageEnglish
Pages (from-to)53-73
Number of pages21
JournalBanach Journal of Mathematical Analysis
Issue number2
Publication statusPublished - 2013
Externally publishedYes


  • Dobrushin ergodicity cofficient
  • L-weak ergodic
  • Uniform ergodic
  • Von neumann algebra
  • Weak ergodic

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory


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