doi:10.1016/j.laa.2018.10.002engAbadias, L.Bonilla, A.Growth orders and ergodicity for absolutely Cesàro bounded operatorsART-2019-108639In 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 <=1, then ‖Tn‖=o(n^α), generalizing the result obtained for α=1. Moreover, if α > 1, then ‖Tn‖=O(n). We apply such results to get stability properties for the Cesàro means of bounded operators.2019http://zaguan.unizar.es/record/8420310.1016/j.laa.2018.10.002http://zaguan.unizar.es/record/84203oai:zaguan.unizar.es:84203LINEAR ALGEBRA AND ITS APPLICATIONS 561 (2019), 253-267by-nc-ndhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccess