000084203 001__ 84203 000084203 005__ 20200716101435.0 000084203 0247_ $$2doi$$a10.1016/j.laa.2018.10.002 000084203 0248_ $$2sideral$$a108639 000084203 037__ $$aART-2019-108639 000084203 041__ $$aeng 000084203 100__ $$0(orcid)0000-0003-2453-7841$$aAbadias, L.$$uUniversidad de Zaragoza 000084203 245__ $$aGrowth orders and ergodicity for absolutely Cesàro bounded operators 000084203 260__ $$c2019 000084203 5060_ $$aAccess copy available to the general public$$fUnrestricted 000084203 5203_ $$aIn 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. 000084203 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/ 000084203 590__ $$a0.988$$b2019 000084203 592__ $$a0.897$$b2019 000084203 591__ $$aMATHEMATICS$$b115 / 324 = 0.355$$c2019$$dQ2$$eT2 000084203 593__ $$aAlgebra and Number Theory$$c2019$$dQ1 000084203 591__ $$aMATHEMATICS, APPLIED$$b157 / 260 = 0.604$$c2019$$dQ3$$eT2 000084203 593__ $$aDiscrete Mathematics and Combinatorics$$c2019$$dQ1 000084203 593__ $$aGeometry and Topology$$c2019$$dQ2 000084203 593__ $$aNumerical Analysis$$c2019$$dQ2 000084203 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000084203 700__ $$aBonilla, A. 000084203 7102_ $$12006$$2015$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Análisis Matemático 000084203 773__ $$g561 (2019), 253-267$$pLinear algebra appl.$$tLINEAR ALGEBRA AND ITS APPLICATIONS$$x0024-3795 000084203 8564_ $$s141183$$uhttps://zaguan.unizar.es/record/84203/files/texto_completo.pdf$$yPostprint 000084203 8564_ $$s68739$$uhttps://zaguan.unizar.es/record/84203/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000084203 909CO $$ooai:zaguan.unizar.es:84203$$particulos$$pdriver 000084203 951__ $$a2020-07-16-08:54:09 000084203 980__ $$aARTICLE