Maximal Inequality Associated to Doubling Condition for State Preserving Actions

2024/07/08 by Bikram, Panchugopal, Saha, Diptesh
#46L40 #46L55 #FOS: Mathematics #Operator Algebras (math.OA) #Primary 46L53 #Secondary 37A55

paper · doi:10.48550/arxiv.2407.05642

Abstract

In this article, we prove maximal inequality and ergodic theorems for state preserving actions on von Neumann algebra by an amenable, locally compact, second countable group equipped with the metric satisfying the doubling condition. The key idea is to use Hardy-Littlewood maximal inequality, a version of the transference principle, and certain norm estimates of differences between ergodic averages and martingales.

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