Noncommutative maximal ergodic inequalities for amenable groups
Abstract
We prove a pointwise ergodic theorem and a maximal inequality for actions of amenable groups on noncommutative measure spaces. To do so, we establish a square function estimate quantifying the difference between ergodic averages and some conditional expectations. Our main technical results are the construction of a well-behaved filtration, based on the quasi-tilings of Ornstein and Weiss, and the square function bound, which we derive from non-doubling noncommutative Calder\'on-Zygmund decomposition. For actions on usual measure spaces, we obtain new variational ergodic inequalities and jump estimates.
Cite
@article{arxiv.2206.12228,
title = {Noncommutative maximal ergodic inequalities for amenable groups},
author = {Léonard Cadilhac and Simeng Wang},
journal= {arXiv preprint arXiv:2206.12228},
year = {2025}
}
Comments
v2: Reorganized and revised with a simplified proof, improved results, and an added appendix; 26 pages. v1:Preliminary version, comments are welcome. 22 pages