Operators acting in the dual spaces of discrete Cesàro spaces

[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(...

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Autores: Bonet Solves, José Antonio|||0000-0002-9096-6380, RICKER, WERNER
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/161155
Acceso en línea:https://riunet.upv.es/handle/10251/161155
Access Level:acceso abierto
Palabra clave:Banach sequence space
Cesaro operator
Regular operator
Multiplier
MATEMATICA APLICADA
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spelling Operators acting in the dual spaces of discrete Cesàro spacesBonet Solves, José Antonio|||0000-0002-9096-6380RICKER, WERNERBanach sequence spaceCesaro operatorRegular operatorMultiplierMATEMATICA APLICADA[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.The research of Prof. Jose Bonet was partially supported by the projects MTM 2016-76647-P and GV Prometeo 2017/102 (Spain).Springer-VerlagDepartamento de Matemática AplicadaEscuela Técnica Superior de ArquitecturaInstituto Universitario de Matemática Pura y AplicadaGeneralitat ValencianaMinisterio de Economía y CompetitividadRepositorio Institucional de la Universitat Politècnica de València Riunet20202020-03-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/161155reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengMinisterio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 MTM2016-76647-P ANALISIS FUNCIONAL, TEORIA DE OPERADORES Y ANALISIS TIEMPO-FRECUENCIAGeneralitat Valenciana https://doi.org/10.13039/501100003359 PROMETEO%2F2017%2F102 ANALISIS FUNCIONAL, TEORIA DE OPERADORES Y APLICACIONESopen accesshttp://purl.org/coar/access_right/c_abf2Reserva de todos los derechoshttp://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1611552026-06-13T07:49:27Z
dc.title.none.fl_str_mv Operators acting in the dual spaces of discrete Cesàro spaces
title Operators acting in the dual spaces of discrete Cesàro spaces
spellingShingle Operators acting in the dual spaces of discrete Cesàro spaces
Bonet Solves, José Antonio|||0000-0002-9096-6380
Banach sequence space
Cesaro operator
Regular operator
Multiplier
MATEMATICA APLICADA
title_short Operators acting in the dual spaces of discrete Cesàro spaces
title_full Operators acting in the dual spaces of discrete Cesàro spaces
title_fullStr Operators acting in the dual spaces of discrete Cesàro spaces
title_full_unstemmed Operators acting in the dual spaces of discrete Cesàro spaces
title_sort Operators acting in the dual spaces of discrete Cesàro spaces
dc.creator.none.fl_str_mv Bonet Solves, José Antonio|||0000-0002-9096-6380
RICKER, WERNER
author Bonet Solves, José Antonio|||0000-0002-9096-6380
author_facet Bonet Solves, José Antonio|||0000-0002-9096-6380
RICKER, WERNER
author_role author
author2 RICKER, WERNER
author2_role author
dc.contributor.none.fl_str_mv Departamento de Matemática Aplicada
Escuela Técnica Superior de Arquitectura
Instituto Universitario de Matemática Pura y Aplicada
Generalitat Valenciana
Ministerio de Economía y Competitividad
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Banach sequence space
Cesaro operator
Regular operator
Multiplier
MATEMATICA APLICADA
topic Banach sequence space
Cesaro operator
Regular operator
Multiplier
MATEMATICA APLICADA
description [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.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-03-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/161155
url https://riunet.upv.es/handle/10251/161155
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 MTM2016-76647-P ANALISIS FUNCIONAL, TEORIA DE OPERADORES Y ANALISIS TIEMPO-FRECUENCIA
Generalitat Valenciana https://doi.org/10.13039/501100003359 PROMETEO%2F2017%2F102 ANALISIS FUNCIONAL, TEORIA DE OPERADORES Y APLICACIONES
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer-Verlag
publisher.none.fl_str_mv Springer-Verlag
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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