Modulated (C,α)-ergodic theorems in noncommutative Lp-spaces

Guixiang Hong; Yuanyuan Jing; Xin Zhang

doi:10.1016/j.jfa.2025.111208

Modulated (C,α)-ergodic theorems in noncommutative L_p-spaces

Guixiang Hong
, Yuanyuan Jing
, Xin Zhang^*

^*Corresponding author for this work

School of Mathematics

Harbin Institute of Technology
Wuhan University

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we first establish the weighted (C,α)[jls-end-space/]-maximal ergodic inequalities for positive Dunford-Schwartz operators acting on noncommutative L_pspaces for α>0 and 1≤p≤∞[jls-end-space/]. Utilizing these results, we then present the noncommutative Besicovitch weighted (C,α)[jls-end-space/]-individual ergodic theorems. Additionally, we also investigate the norm convergence of the Besicovitch weighted (C,α)[jls-end-space/]-ergodic averages. Some of them appear to be new even in the commutative setting.

Original language	English
Article number	111208
Journal	Journal of Functional Analysis
Volume	290
Issue number	1
DOIs	https://doi.org/10.1016/j.jfa.2025.111208
State	Published - 1 Jan 2026

Keywords

Besicovitch sequences
Maximal ergodic inequalities
NoncommutativeL-spaces
Weighted (C,α)-individual ergodic theorems

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10.1016/j.jfa.2025.111208

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title = "Modulated (C,α)-ergodic theorems in noncommutative Lp-spaces",

abstract = "In this paper, we first establish the weighted (C,α)[jls-end-space/]-maximal ergodic inequalities for positive Dunford-Schwartz operators acting on noncommutative Lpspaces for α>0 and 1≤p≤∞[jls-end-space/]. Utilizing these results, we then present the noncommutative Besicovitch weighted (C,α)[jls-end-space/]-individual ergodic theorems. Additionally, we also investigate the norm convergence of the Besicovitch weighted (C,α)[jls-end-space/]-ergodic averages. Some of them appear to be new even in the commutative setting.",

keywords = "Besicovitch sequences, Maximal ergodic inequalities, NoncommutativeL-spaces, Weighted (C,α)-individual ergodic theorems",

author = "Guixiang Hong and Yuanyuan Jing and Xin Zhang",

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T1 - Modulated (C,α)-ergodic theorems in noncommutative Lp-spaces

AU - Hong, Guixiang

AU - Jing, Yuanyuan

AU - Zhang, Xin

PY - 2026/1/1

Y1 - 2026/1/1

N2 - In this paper, we first establish the weighted (C,α)[jls-end-space/]-maximal ergodic inequalities for positive Dunford-Schwartz operators acting on noncommutative Lpspaces for α>0 and 1≤p≤∞[jls-end-space/]. Utilizing these results, we then present the noncommutative Besicovitch weighted (C,α)[jls-end-space/]-individual ergodic theorems. Additionally, we also investigate the norm convergence of the Besicovitch weighted (C,α)[jls-end-space/]-ergodic averages. Some of them appear to be new even in the commutative setting.

AB - In this paper, we first establish the weighted (C,α)[jls-end-space/]-maximal ergodic inequalities for positive Dunford-Schwartz operators acting on noncommutative Lpspaces for α>0 and 1≤p≤∞[jls-end-space/]. Utilizing these results, we then present the noncommutative Besicovitch weighted (C,α)[jls-end-space/]-individual ergodic theorems. Additionally, we also investigate the norm convergence of the Besicovitch weighted (C,α)[jls-end-space/]-ergodic averages. Some of them appear to be new even in the commutative setting.

KW - Besicovitch sequences

KW - Maximal ergodic inequalities

KW - NoncommutativeL-spaces

KW - Weighted (C,α)-individual ergodic theorems

UR - https://www.scopus.com/pages/publications/105017922007

U2 - 10.1016/j.jfa.2025.111208

DO - 10.1016/j.jfa.2025.111208

M3 - 文章

AN - SCOPUS:105017922007

SN - 0022-1236

VL - 290

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 1

M1 - 111208

ER -

Modulated (C,α)-ergodic theorems in noncommutative L_p-spaces

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