Power bounded operators and the mean ergodic theorem for subsequences

Tanja Eisner; Vladimir Müller

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arXiv · 2001.05804

Power bounded operators and the mean ergodic theorem for subsequences

Tanja Eisner·Vladimir Müller

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Abstract

Let $T$ be a power bounded Hilbert space operator without unimodular eigenvalues. We show that the subsequential ergodic averages $N^{-1}\sum_{n=1}^N T^{a_n}$ 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 $N^{-1}\sum_{n=1}^N e^{2\pi i g(n)}T^{a_n}$ 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 \cite{tEM} to real polynomials and polynomial weights.

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Tanja Eisner, Vladimir Müller. 2020-01-16. Power bounded operators and the mean ergodic theorem for subsequences. https://arxiv.org/abs/2001.05804

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