Work

Noncommutative maximal ergodic inequalities for amenable groups

Year: 2022

Type: preprint

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 Calderón-Zygmund decomposition. For actions on usual measure spaces, we obtain new variational ergodic inequalities and jump estimates.

Source: HAL (Le Centre pour la Communication Scientifique Directe)

DOI: 10.48550/arxiv.2206.12228

Authors: Cadilhac, Léonard, Wang, Simeng

Institutions: Institut de Mathématiques de Jussieu-Paris Rive Gauche, Sorbonne Université, Harbin Institute of Technology

Language: English

Topic: Advanced Operator Algebra Research

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Agence Nationale de la Recherche, National Natural Science Foundation of China, Fondation Mathématique Jacques Hadamard, Fundamental Research Funds for the Central Universities

Awards: G2054192911, G3010527862, G6845737225, Noncommutative analysis on groups and quantum groups

OpenAlex ID: W4320085737

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