A Few Remarks on Asymptotic Stabilities of Markov Operators on L1-Spaces

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Abstract

Abstract: In this paper, the investigation of a generalized Dobrushin ergodicity coefficient to obtain uniform ergodicity and uniform mean ergodicities of positive contractions of L1-spaces is carried out. Through the introduction of notions such as mean P-completely mixing and P-completely mixing, the last one being an extension of the complete mixing, several analogues of the Akcoglu and Sucheston theorem are proved. As an applications of these results, we establish mean ergodicities of positive contractions of L1-spaces. It is vital to note that P stands for a Markov projection of L1.

Original languageEnglish
Pages (from-to)3173-3183
Number of pages11
JournalLobachevskii Journal of Mathematics
Volume42
Issue number13
DOIs
Publication statusPublished - Dec 2021

Keywords

  • Dobrushin ergodicity coefficient
  • Markov operator
  • P-completely mixing
  • positive contraction
  • uniform ergodicity

ASJC Scopus subject areas

  • General Mathematics

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