Noncommutative maximal ergodic inequalities for amenable groups

Autor:	Cadilhac, Léonard, Wang, Simeng
Rok vydání:	2022
Předmět:	Mathematics - Operator Algebras Mathematics - Dynamical Systems Mathematics - Functional Analysis Mathematics - Group Theory
Druh dokumentu:	Working Paper
Popis:	We prove a pointwise ergodic theorem for actions of amenable groups on noncommutative measure spaces. To do so, we establish the maximal ergodic inequality for averages of operator-valued functions on amenable groups. The main arguments are a geometric construction of martingales based on the Ornstein-Weiss quasi-tilings and harmonic analytic estimates coming from noncommutative Calder\'on-Zygmund theory. Comment: Preliminary version, comments are welcome. 22 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2206.12228 Zobrazit plný text záznamu View this record from Arxiv