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A. L. Bernardis, M. Lorente, F. J. Martín-Reyes, A. de la Torre, M. T. Martínez, DIFFERENCES OF ERGODIC AVERAGES FOR CESÀRO BOUNDED OPERATORS, The Quarterly Journal of Mathematics, Volume 58, Issue 2, June 2007, Pages 137–150, https://doi.org/10.1093/qmath/hal023
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Abstract
We prove that the weighted differences of ergodic averages, induced by a Cesàro bounded, strongly continuous, one-parameter group of positive, invertible, linear operators on Lp, 1 < p < ∞, converge almost every where and in the Lp-norm. We obtain first the boundedness of the ergodic maximal operator and the convergence of the averages.
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