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Ergodic sequences of averages of group representations

Published online by Cambridge University Press:  19 September 2008

Michael Lin  and
Rainer Wittmann
Michael Lin
Affiliation:
Department of Mathematics, Ben-Gurion University of the Negev Beer-Sheva, Israel
Rainer Wittmann
Affiliation:
Institut für Mathematische Stochastik, Lotzestrasse 13, Gottingen, Germany
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Abstract

Let G be a locally compact σ -compact group with right Haar measure λ. A sequence {μn} of probabilities on G is called ergodic if for every f ∈ L1(G, λ) and t ∈ G we have ‖μn* (f − δt* f) ‖1 → 0. If T (t) is a bounded continuous representation of G by linear operators in a Banach space X, we define the μ,-average of T(t) by .

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 14 , Issue 1 , March 1994 , pp. 181 - 196
Copyright
Copyright © Cambridge University Press 1994

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