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arXiv · 1207.5835

Almost weak polynomial stability of operators

Dávid Kunszenti-Kovács
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Abstract

We investigate whether almost weak stability of an operator $T$ on a Banach space $X$ implies its almost weak polynomial stability. We show, using a modified version of the van der Corput Lemma that if $X$ is a Hilbert space and $T$ a contraction, then the implication holds. On the other hand, based on a TDS arising from a two dimensional ODE, we give an explicit example of a contraction on a $C_0$ space that is almost weakly stable, but its appropriate polynomial powers fail to converge weakly to zero along a subsequence of density 1. Finally we provide an application to convergence of polynomial multiple ergodic averages.

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Dávid Kunszenti-Kovács. 2013-06-21. Almost weak polynomial stability of operators. https://arxiv.org/abs/1207.5835

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