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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