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Cesaro bounded operators in Banach spaces

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Cesaro bounded operators in Banach spaces

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dc.contributor.author Bermúdez, Teresa es_ES
dc.contributor.author Bonilla, Antonio es_ES
dc.contributor.author Muller, Vladimir es_ES
dc.contributor.author Peris Manguillot, Alfredo es_ES
dc.date.accessioned 2021-07-20T03:30:46Z
dc.date.available 2021-07-20T03:30:46Z
dc.date.issued 2020-03 es_ES
dc.identifier.issn 0021-7670 es_ES
dc.identifier.uri http://hdl.handle.net/10251/169537
dc.description.abstract [EN] We study several notions of boundedness for operators. It is known that any power bounded operator is absolutely Cesaro bounded and strongly Kreiss bounded (in particular, uniformly Kreiss bounded). The converses do not hold in general. In this note, we give examples of topologically mixing (hence, not power bounded) absolutely Cesaro bounded operators on l(p)(N), 1 <= p < infinity, and provide examples of uniformly Kreiss bounded operators which are not absolutely Cesaro bounded. These results complement a few known examples (see [27] and [2]). We also obtain a characterization of power bounded operators which generalizes a result of Van Casteren [32]. In [2] Aleman and Suciu asked if every uniformly Kreiss bounded operator T on a Banach space satisfies that. We solve this question for Hilbert space operators and, moreover, we prove that, if T is absolutely Cesaro bounded on a Banach (Hilbert) space, then parallel to T-n parallel to = o(n) ((parallel to Tn parallel to=o(n12), respectively). As a consequence, every absolutely Cesaro bounded operator on a reflexive Banach space is mean ergodic. es_ES
dc.description.sponsorship The first, second and fourth authors were supported by MINECO and FEDER, Project MTM201675963-P. The third author was supported by grant No. 17-27844S of GA CR and RVO: 67985840. The fourth author was also supported by Generalitat Valenciana, Project PROMETEO/2017/102. es_ES
dc.language Inglés es_ES
dc.publisher Springer-Verlag es_ES
dc.relation.ispartof Journal d Analyse Mathématique es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Cesàro bounded operators es_ES
dc.subject Kreiss bounded operators es_ES
dc.subject Mean ergodic operators es_ES
dc.subject Mixing es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Cesaro bounded operators in Banach spaces es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1007/s11854-020-0085-8 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/GACR//17-27844S/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/GACR//67985840/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/MINECO//MTM2016-75963-P/ES/DINAMICA DE OPERADORES/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/GVA//PROMETEO%2F2017%2F102/ES/ANALISIS FUNCIONAL, TEORIA DE OPERADORES Y APLICACIONES/ es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.description.bibliographicCitation Bermúdez, T.; Bonilla, A.; Muller, V.; Peris Manguillot, A. (2020). Cesaro bounded operators in Banach spaces. Journal d Analyse Mathématique. 140(1):187-206. https://doi.org/10.1007/s11854-020-0085-8 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.1007/s11854-020-0085-8 es_ES
dc.description.upvformatpinicio 187 es_ES
dc.description.upvformatpfin 206 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 140 es_ES
dc.description.issue 1 es_ES
dc.relation.pasarela S\435013 es_ES
dc.contributor.funder Czech Grant Agency es_ES
dc.contributor.funder Generalitat Valenciana es_ES
dc.contributor.funder European Regional Development Fund es_ES
dc.contributor.funder Ministerio de Economía y Competitividad es_ES
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