Noncommutative weighted individual ergodic theorems with continuous time

Vladimir Chilin, Semyon Litvinov

Research output: Contribution to journalArticlepeer-review

Abstract

We show that ergodic flows in the noncommutative L1-space (associated with a semifinite von Neumann algebra) generated by continuous semigroups of positive Dunford-Schwartz operators and modulated by bounded Besicovitch almost periodic functions converge almost uniformly. The corresponding local ergodic theorem is also proved. We then extend these results to arbitrary noncommutative fully symmetric spaces and present applications to noncommutative Orlicz (in particular, noncommutative Lp-spaces), Lorentz, and Marcinkiewicz spaces. The commutative counterparts of the results are derived.

Original languageEnglish (US)
Article number2050013
JournalInfinite Dimensional Analysis, Quantum Probability and Related Topics
Volume23
Issue number2
DOIs
StatePublished - Jun 1 2020

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Mathematical Physics
  • Applied Mathematics

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