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A quantitative mean ergodic theorem for uniformly convex Banach spaces

Published online by Cambridge University Press:  17 March 2009

U. KOHLENBACH  and
L. LEUŞTEAN
U. KOHLENBACH
Affiliation:
Department of Mathematics, Technische Universität Darmstadt, Schlossgartenstrasse 7, 64289 Darmstadt, Germany (email: kohlenbach@mathematik.tu-darmstadt.de)
L. LEUŞTEAN
Affiliation:
Department of Mathematics, Technische Universität Darmstadt, Schlossgartenstrasse 7, 64289 Darmstadt, Germany (email: kohlenbach@mathematik.tu-darmstadt.de) Institute of Mathematics ‘Simion Stoilow’ of the Romanian Academy, Calea Griviţei 21, PO Box 1-462, Bucharest, Romania (email: leustean@mathematik.tu-darmstadt.de)
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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 Tao of the mean ergodic theorem for such spaces and so generalizes similar results obtained for Hilbert spaces by Avigad et al [Local stability of ergodic averages. Trans. Amer. Math. Soc. to appear] and Tao [Norm convergence of multiple ergodic averages for commuting transformations. Ergod. Th. & Dynam. Sys.28(2) (2008), 657–688].

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 29 , Issue 6 , December 2009 , pp. 1907 - 1915
Copyright
Copyright © Cambridge University Press 2009

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References

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