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arXiv · 1710.02981

Growth orders and ergodicity for absolutely Cesàro bounded operators

Luciano Abadias·Antonio Bonilla
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Abstract

In this paper, we extend the concept of absolutely Cesàro boundedness to the fractional case. We construct a weighted shift operator belonging to this class of operators, and we prove that if $T$ is an absolutely Cesàro bounded operator of order $α$ with $0<α\le 1,$ then $\| T^n\|=o(n^α)$, generalizing the result obtained for $α=1$. Moreover, if $α> 1$, then $\|T^{n}\|= O(n)$. We apply such results to get stability properties for the Cesàro means of bounded operators.

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Luciano Abadias, Antonio Bonilla. 2017-10-09. Growth orders and ergodicity for absolutely Cesàro bounded operators. https://arxiv.org/abs/1710.02981

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