Differences of ergodic averages for Cesaro bounded operators

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. © 2007. Published by Oxford University Press. All rights reserved.