The Fréchet space ces(p+), 1 <
[EN] The Banach spaces ces(p), 1 < p < infinity, were intensively studied by G. Bennett and others. The largest solid Banach lattice in C-N which contains l(p) and which the Cesaro operator C : C-N -> C-N maps into l(P) is ces(p). For each 1 <= p < infinity, the (p...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2018 |
| 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:10251/107410 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/107410 |
| Access Level: | acceso abierto |
| Palabra clave: | Fréchet spaces sequence spaces power series spaces Schwartz spaces Fréchet lattices MATEMATICA APLICADA |
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The Fréchet space ces(p+), 1 <p <inftyAlbanese, AngelaRicker, Werner J.Bonet Solves, José Antonio|||0000-0002-9096-6380Fréchet spacessequence spacespower series spacesSchwartz spacesFréchet latticesMATEMATICA APLICADA[EN] The Banach spaces ces(p), 1 < p < infinity, were intensively studied by G. Bennett and others. The largest solid Banach lattice in C-N which contains l(p) and which the Cesaro operator C : C-N -> C-N maps into l(P) is ces(p). For each 1 <= p < infinity, the (positive) operator C also maps the Frechet space l(p+) = boolean AND(q > p) l(q) into itself. It is shown that the largest solid Frechet lattice in C-N which contains l(p+) and which C maps into l(p+) is precisely ces(p+) := boolean AND(q > p) ces(q). Although the spaces l(p+) are well understood, it seems that the spaces ces(p+) have not been considered at all. A detailed study of the Frechet spaces ces(p+),1 <= p < infinity, is undertaken. They are very different to the Frechet spaces l(p+) which generate them in the above sense. We prove that each ces(p+) is a power series space of finite type and order one, and that all the spaces ces(p+), 1 <= p < infinity, are isomorphic. (C) 2017 Elsevier Inc. All rights reserved.The authors thank the referee for a considerable simplification of some proofs in Section 3. The research of the first two authors was partially supported by the project MTM2016-76647-P (Spain). The second author thanks the Mathematics Department of the Katholische Universitat Eichstatt-Ingolstadt (Germany) for its support and hospitality during his research visit in the period September 2016 July 2017.ElsevierDepartamento de Matemática AplicadaEscuela Técnica Superior de ArquitecturaInstituto Universitario de Matemática Pura y AplicadaMinisterio de Economía y CompetitividadRepositorio Institucional de la Universitat Politècnica de València Riunet20182018-01-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/107410reponame: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-FRECUENCIAopen accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1074102026-06-13T07:49:27Z |
| dc.title.none.fl_str_mv |
The Fréchet space ces(p+), 1 < p < infty |
| title |
The Fréchet space ces(p+), 1 < |
| spellingShingle |
The Fréchet space ces(p+), 1 < Albanese, Angela Fréchet spaces sequence spaces power series spaces Schwartz spaces Fréchet lattices MATEMATICA APLICADA |
| title_short |
The Fréchet space ces(p+), 1 < |
| title_full |
The Fréchet space ces(p+), 1 < |
| title_fullStr |
The Fréchet space ces(p+), 1 < |
| title_full_unstemmed |
The Fréchet space ces(p+), 1 < |
| title_sort |
The Fréchet space ces(p+), 1 < |
| dc.creator.none.fl_str_mv |
Albanese, Angela Ricker, Werner J. Bonet Solves, José Antonio|||0000-0002-9096-6380 |
| author |
Albanese, Angela |
| author_facet |
Albanese, Angela Ricker, Werner J. Bonet Solves, José Antonio|||0000-0002-9096-6380 |
| author_role |
author |
| author2 |
Ricker, Werner J. Bonet Solves, José Antonio|||0000-0002-9096-6380 |
| author2_role |
author author |
| dc.contributor.none.fl_str_mv |
Departamento de Matemática Aplicada Escuela Técnica Superior de Arquitectura Instituto Universitario de Matemática Pura y Aplicada Ministerio de Economía y Competitividad Repositorio Institucional de la Universitat Politècnica de València Riunet |
| dc.subject.none.fl_str_mv |
Fréchet spaces sequence spaces power series spaces Schwartz spaces Fréchet lattices MATEMATICA APLICADA |
| topic |
Fréchet spaces sequence spaces power series spaces Schwartz spaces Fréchet lattices MATEMATICA APLICADA |
| description |
[EN] The Banach spaces ces(p), 1 < p < infinity, were intensively studied by G. Bennett and others. The largest solid Banach lattice in C-N which contains l(p) and which the Cesaro operator C : C-N -> C-N maps into l(P) is ces(p). For each 1 <= p < infinity, the (positive) operator C also maps the Frechet space l(p+) = boolean AND(q > p) l(q) into itself. It is shown that the largest solid Frechet lattice in C-N which contains l(p+) and which C maps into l(p+) is precisely ces(p+) := boolean AND(q > p) ces(q). Although the spaces l(p+) are well understood, it seems that the spaces ces(p+) have not been considered at all. A detailed study of the Frechet spaces ces(p+),1 <= p < infinity, is undertaken. They are very different to the Frechet spaces l(p+) which generate them in the above sense. We prove that each ces(p+) is a power series space of finite type and order one, and that all the spaces ces(p+), 1 <= p < infinity, are isomorphic. (C) 2017 Elsevier Inc. All rights reserved. |
| publishDate |
2018 |
| dc.date.none.fl_str_mv |
2018 2018-01-01 |
| 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/10251/107410 |
| url |
https://riunet.upv.es/handle/10251/107410 |
| 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 |
| dc.rights.none.fl_str_mv |
open access http://purl.org/coar/access_right/c_abf2 Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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info:eu-repo/semantics/openAccess |
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open access http://purl.org/coar/access_right/c_abf2 Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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openAccess |
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application/pdf application/pdf |
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Elsevier |
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Elsevier |
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reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia instname:Universitat Politècnica de València (UPV) |
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Universitat Politècnica de València (UPV) |
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RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
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RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
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