A quantitative Mean Ergodic Theorem for uniformly convex Banach spaces

2008/04/24 by Ulrich Kohlenbach, Kohlenbach, Ulrich, Laurenţiu Leuştean +1
Computer Science · Mathematics · #Advanced Banach Space Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Logic (math.LO) #Markov Chains and Monte Carlo Methods #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.0804.3844

openalex publication_date 2008/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide an explicit uniform bound on the local stability of ergodic averages in uniformly convex Banach spaces. Our result can also be viewed as a finitary version in the sense of T. Tao of the Mean Ergodic Theorem for such spaces and so generalizes similar results obtained for Hilbert spaces by Avigad, Gerhardy and Towsner (arXiv:0706.1512v2 [math.DS]) and T. Tao (arXiv:0707.1117v1 [math.DS]).

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