Noncommutative weighted individual ergodic theorems with continuous time

<jats:p> We show that ergodic flows in the noncommutative [Formula: see text]-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 [Formula: see text]-spaces), Lorentz, and Marcinkiewicz spaces. The commutative counterparts of the results are derived. /jats:p

Electronic version of an article published as 'Infinite Dimensional Analysis, Quantum Probability and Related Topics', 23, 02, 2020, 2050013 10.1142/s0219025720500137 © World Scientific Publishing Company https://doi.org/10.1142/s0219025720500137

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Work Title Noncommutative weighted individual ergodic theorems with continuous time
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Open Access
Creators
  1. Vladimir Chilin
  2. Semyon Litvinov
License In Copyright (Rights Reserved)
Work Type Article
Publisher
  1. World Scientific Pub Co Pte Lt
Publication Date June 2020
Publisher Identifier (DOI)
  1. 10.1142/s0219025720500137
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  1. Infinite Dimensional Analysis, Quantum Probability and Related Topics
Deposited January 13, 2022

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