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Operators acting in the dual spaces of discrete Cesàro spaces

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Operators acting in the dual spaces of discrete Cesàro spaces

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dc.contributor.author Bonet Solves, José Antonio es_ES
dc.contributor.author RICKER, WERNER es_ES
dc.date.accessioned 2021-02-12T04:31:01Z
dc.date.available 2021-02-12T04:31:01Z
dc.date.issued 2020-03 es_ES
dc.identifier.issn 0026-9255 es_ES
dc.identifier.uri http://hdl.handle.net/10251/161155
dc.description.abstract [EN] The discrete Cesaro (Banach) sequence spaces ces(r),1<r<infinity, have been thoroughly investigated for over 45 years. Not so for their dual spaces d(s) approximately equal to (ces(r))', which are somewhat unwieldy. Our aim is to undertake a further study of the spaces d(s) and of various operators acting between these spaces. It is shown that d(s)subset of d(t) whenever s <= t, with the inclusion being compact if s<t.The classical Cesaro operator C is continuous from d(s) into d(t) precisely when s <= t and compact precisely when s<t. Moreover, C even maps the larger space ces(s) continuously into d(s). This is a consequence of the Hardy-Littlewood maximal theorem and the remarkable property, for each 1<s<infinity, that x is an element of CN if and only if C(|x|)is an element of d(s). These results are used to analyze the spectrum and to determine the norm and the mean ergodicity of C acting in d(s). Similar properties for multiplier operators are also treated. es_ES
dc.description.sponsorship The research of Prof. Jose Bonet was partially supported by the projects MTM 2016-76647-P and GV Prometeo 2017/102 (Spain). es_ES
dc.language Inglés es_ES
dc.publisher Springer-Verlag es_ES
dc.relation.ispartof Monatshefte für Mathematik es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Banach sequence space es_ES
dc.subject Cesaro operator es_ES
dc.subject Regular operator es_ES
dc.subject Multiplier es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Operators acting in the dual spaces of discrete Cesàro spaces es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1007/s00605-020-01370-2 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/MINECO//MTM2016-76647-P/ES/ANALISIS FUNCIONAL, TEORIA DE OPERADORES Y ANALISIS TIEMPO-FRECUENCIA/ 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 Bonet Solves, JA.; Ricker, W. (2020). Operators acting in the dual spaces of discrete Cesàro spaces. Monatshefte für Mathematik. 191(3):487-512. https://doi.org/10.1007/s00605-020-01370-2 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.1007/s00605-020-01370-2 es_ES
dc.description.upvformatpinicio 487 es_ES
dc.description.upvformatpfin 512 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 191 es_ES
dc.description.issue 3 es_ES
dc.relation.pasarela S\405035 es_ES
dc.contributor.funder Generalitat Valenciana es_ES
dc.contributor.funder Ministerio de Economía y Competitividad es_ES
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