Power bounded operators and the mean ergodic theorem for subsequences

2020/01/16 by Eisner, Tanja, Müller, Vladimir
#Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2001.05804

Abstract

Let T be a power bounded Hilbert space operator without unimodular eigenvalues. We show that the subsequential ergodic averages N^-1∑_n=1^N T^a_n converge in the strong operator topology for a wide range of sequences (a_n), including the integer part of most of subpolynomial Hardy functions. Moreover, we show that the weighted averages N^-1∑_n=1^N e^{2πi g(n)}T^a_n also converge for many reasonable functions g. In particular, we generalize the polynomial mean ergodic theorem for power bounded operators due to ter Elst and the second author \citetEM to real polynomials and polynomial weights.

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