Order convergence ergodic theorems in rearrangement invariant spaces

Mustafa Muratov, Julia Pashkova, Ben Zion Rubshtein

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

We find necessary and sufficient conditions for order convergence of Cesáro averages of positive absolute contractions in rearrangement invariant spaces. We study the case, when the considered measure is infinite. The investigation of order convergence includes both Dominated and Individual Ergodic Theorems.

Original languageEnglish
Title of host publicationOperator Methods in Mathematical Physics - Conference on Operator Theory, Analysis and Mathematical Physics, OTAMP 2010
EditorsJan Janas, Pavel Kurasov, Ari Laptev, Sergei Naboko
PublisherSpringer International Publishing
Pages123-142
Number of pages20
ISBN (Print)9783034805308
DOIs
StatePublished - 1 Jan 2013
Event5th International Conference: Operator Theory, Analysis and Mathematical Physics, OTAMP 2010 - Bedlewo, Poland
Duration: 5 Aug 201012 Aug 2010

Publication series

NameOperator Theory: Advances and Applications
Volume227
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878

Conference

Conference5th International Conference: Operator Theory, Analysis and Mathematical Physics, OTAMP 2010
Country/TerritoryPoland
CityBedlewo
Period5/08/1012/08/10

Keywords

  • Ergodic theorems
  • Order convergence
  • Positive absolute contraction
  • Rearrangement invariant spaces

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