Noncommutative Maximal Ergodic Theorems for Modulated (C,α)-Averages with Operator-Valued Weights
Abstract
In this paper, we study modulated (C,α)-ergodic averages with operator-valued weights and their subsequential versions in the setting of semifinite von Neumann algebras. Our framework combines (C,α)-type modulation with operator-valued weights and extends both scalar-weighted and operator-valued weighted ergodic theories. We establish mean ergodic theorems and maximal inequalities for these averages on noncommutative Lp-spaces. We then study bilateral almost uniform and almost uniform convergence in noncommutative Orlicz spaces, including convergence along subsequences of density one. A key ingredient in our approach is the introduction of the p-convexity condition on the underlying Orlicz function. This condition enables us to transfer appropriate maximal estimates from noncommutative Lp-spaces to establish bilateral uniform equicontinuity in measure at zero on the corresponding noncommutative p-convex Orlicz spaces. Together with the noncommutative Banach principle, this yields the desired pointwise convergence results. As an additional consequence of our p-convexity argument, we extend Rota's theorem to a larger class of noncommutative Orlicz spaces associated with the p-convex Orlicz functions considered in this article.
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BibTeX
@misc{chattopadhyay2026noncommutative,
title = {{Noncommutative Maximal Ergodic Theorems for Modulated $(C,α)$-Averages with Operator-Valued Weights}},
author = {Arup Chattopadhyay and Debabrata De and Disha Shaw},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23616},
eprint = {2609.23616},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23616},
}
RIS
TY - UNPB
TI - Noncommutative Maximal Ergodic Theorems for Modulated (C,α)-Averages with Operator-Valued Weights
AU - Arup Chattopadhyay
AU - Debabrata De
AU - Disha Shaw
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2609.23616
UR - https://arxiv.org/abs/2609.23616
AB - In this paper, we study modulated (C,α)-ergodic averages with operator-valued weights and their subsequential versions in the setting of semifinite von Neumann algebras. Our framework combines (C,α)-type modulation with operator-valued weights and extends both scalar-weighted and operator-valued weighted ergodic theories. We establish mean ergodic theorems and maximal inequalities for these averages on noncommutative L_p-spaces. We then study bilateral almost uniform and almost uniform convergence in noncommutative Orlicz spaces, including convergence along subsequences of density one. A key ingredient in our approach is the introduction of the p-convexity condition on the underlying Orlicz function. This condition enables us to transfer appropriate maximal estimates from noncommutative L_p-spaces to establish bilateral uniform equicontinuity in measure at zero on the corresponding noncommutative p-convex Orlicz spaces. Together with the noncommutative Banach principle, this yields the desired pointwise convergence results. As an additional consequence of our p-convexity argument, we extend Rota's theorem to a larger class of noncommutative Orlicz spaces associated with the p-convex Orlicz functions considered in this article.
ER -