RT info:eu-repo/semantics/article
T1 Cesàro bounded operators in Banach spaces
A1 Bermúdez De León, Teresa De Jesús
A1 Bonilla Ramírez, Antonio Lorenzo
A1 Müller, V.
A1 Peris, A.
K1 Banach spaces
AB Westudyseveralnotionsofboundedness foroperators. It isknownthat anypowerboundedoperatorisabsolutelyCes`aroboundedandstronglyKreiss bounded(inparticular,uniformlyKreissbounded).Theconversesdonothold ingeneral. Inthisnote,wegiveexamplesoftopologicallymixing(hence,not powerbounded)absolutelyCes`aroboundedoperatorson p(N),1≤p<∞, andprovideexamplesofuniformlyKreissboundedoperatorswhicharenot absolutelyCes`arobounded.Theseresultscomplementafewknownexamples (see [27] and [2]). Wealsoobtainacharacterizationof powerboundedoperatorswhichgeneralizesaresultofVanCasteren [32]. In [2]Alemanand SuciuaskedifeveryuniformlyKreissboundedoperatorTonaBanachspace satisfiesthat limn→∞ Tn n =0.WesolvethisquestionforHilbertspaceoperatorsand,moreover,weprovethat, ifT isabsolutelyCes`aroboundedona Banach(Hilbert)space,then Tn =o(n)( Tn =o(n1 2),respectively).Asa consequence,everyabsolutelyCes`aroboundedoperatoronareflexiveBanach spaceismeanergodic.
YR 2020
FD 2020
LK http://riull.ull.es/xmlui/handle/915/35511
UL http://riull.ull.es/xmlui/handle/915/35511
LA en
DS Repositorio institucional de la Universidad de La Laguna
RD 19-oct-2024