Fluctuation bounds for ergodic averages of amenable groups on uniformly\n convex Banach spaces

2019/01/24 by Andrew Warren, Warren, Andrew
Mathematics · #37A30 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1901.08538

openalex publication_date 2019/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study fluctuations of ergodic averages generated by actions of amenable\ngroups. In the setting of an abstract ergodic theorem for locally compact\nsecond countable amenable groups acting on uniformly convex Banach spaces, we\ndeduce a highly uniform bound on the number of fluctuations of the ergodic\naverage for a class of F olner sequences satisfying an analogue of\nLindenstrauss's temperedness condition. Equivalently, we deduce a uniform bound\non the number of fluctuations over long distances for arbitrary F olner\nsequences. As a corollary, these results imply associated bounds for a\ncontinuous action of an amenable group on a \σ-finite L^p space with\np\∈(1,\∞).\n

Citations

• Nonstandard Convergence Gives Bounds on Jumps

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