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Two Consequences of Brunel's Theorem
Published online by Cambridge University Press: 20 November 2018
Abstract
In this note we observe two consequences of Brunei's recent theorem. If T1,..., Tn are majorized by positive power-bounded operators S1,..., Sn of Lp, 1 < p < ∞, for which the ergodic theorem holds, then a multiple sequence ergodic theorem holds for T1,....,Tn. Further, the individual convergence for each Tk can be taken along uniform sequences.
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- Copyright © Canadian Mathematical Society 1991