Completeness in the Mackey topology by norming subspaces
[EN] We study the class of Banach spaces X such that the locally convex space (X, mu(X,Y)) is complete for every norming and norm-closed subspace Y subset of X*, where mu(X, Y) denotes the Mackey topology on X associated to the dual pair < X, Y >. Such Banach spaces are called fully Ma...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2019 |
| 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:10251/155855 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/155855 |
| Access Level: | acceso abierto |
| Palabra clave: | Mackey topology Completeness Norming subspace Mazur property MATEMATICA APLICADA |
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Completeness in the Mackey topology by norming subspacesGuirao Sánchez, Antonio José|||0000-0002-1031-3954Martínez-Cervantes, G.Rodríguez Ruiz, JoséMackey topologyCompletenessNorming subspaceMazur propertyMATEMATICA APLICADA[EN] We study the class of Banach spaces X such that the locally convex space (X, mu(X,Y)) is complete for every norming and norm-closed subspace Y subset of X*, where mu(X, Y) denotes the Mackey topology on X associated to the dual pair < X, Y >. Such Banach spaces are called fully Mackey complete. We show that fully Mackey completeness is implied by Efremov's property (epsilon) and, on the other hand, it prevents the existence of subspaces isomorphic to l(1)(omega(1)). This extends previous results by Guirao et al. (2017) [9] and Bonet and Cascales (2010) [3]. Further examples of Banach spaces which are not fully Mackey complete are exhibited, like C[0, omega(1)] and the long James space J(omega(1)). Finally, by assuming the Continuum Hypothesis, we construct a Banach space with w*-sequential dual unit ball which is not fully Mackey complete. A key role in our discussion is played by the (at least formally) smaller class of Banach spaces X such that (Y, w*) has the Mazur property for every norming and norm-closed subspace Y subset of X*. (C) 2019 Elsevier Inc. All rights reserved.The authors wish to thank A. Aviles for valuable discussions on the topic of this paper. They are also grateful to the referee for his/her comments and suggestions. A.J. Guirao was supported by projects MTM2017-83262-C2-1-P (AEI/FEDER, UE) and 19368/PI/14 (Fundacion Seneca). G. Martinez-Cervantes and J. Rodriguez were supported by projects MTM2014-54182-P and MTM2017-86182-P (AEI/FEDER, UE) and 19275/PI/14 (Fundacion Seneca).ElsevierEscuela Técnica Superior de Ingeniería de TelecomunicaciónDepartamento de Matemática AplicadaInstituto Universitario de Matemática Pura y AplicadaEuropean Regional Development FundMinisterio de Economía y CompetitividadFundación Séneca-Agencia de Ciencia y Tecnología de la Región de MurciaAgencia Estatal de InvestigaciónRepositorio Institucional de la Universitat Politècnica de València Riunet20192019-10-15journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/155855reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016 MTM2017-83262-C2-1-P ANALISIS COMPLEJO Y GEOMETRIA EN ESPACIOS DE BANACHAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016 MTM2017-83262-C2-2-P LA INTERACCION ENTRE GEOMETRIA Y TOPOLOGIA EN ESPACIOS DE BANACH. APLICACIONES.Fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia https://doi.org/10.13039/100007801 19368%2FPI%2F14Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016 MTM2017-86182-P TEORIA DE CONJUNTOS Y ESPACIOS DE BANACHMinisterio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 MTM2014-54182-P TOPOLOGIA, ANALISIS Y CONJUNTOSFundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia https://doi.org/10.13039/100007801 19275%2FPI%2F14open 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:10251/1558552026-06-13T07:49:27Z |
| dc.title.none.fl_str_mv |
Completeness in the Mackey topology by norming subspaces |
| title |
Completeness in the Mackey topology by norming subspaces |
| spellingShingle |
Completeness in the Mackey topology by norming subspaces Guirao Sánchez, Antonio José|||0000-0002-1031-3954 Mackey topology Completeness Norming subspace Mazur property MATEMATICA APLICADA |
| title_short |
Completeness in the Mackey topology by norming subspaces |
| title_full |
Completeness in the Mackey topology by norming subspaces |
| title_fullStr |
Completeness in the Mackey topology by norming subspaces |
| title_full_unstemmed |
Completeness in the Mackey topology by norming subspaces |
| title_sort |
Completeness in the Mackey topology by norming subspaces |
| dc.creator.none.fl_str_mv |
Guirao Sánchez, Antonio José|||0000-0002-1031-3954 Martínez-Cervantes, G. Rodríguez Ruiz, José |
| author |
Guirao Sánchez, Antonio José|||0000-0002-1031-3954 |
| author_facet |
Guirao Sánchez, Antonio José|||0000-0002-1031-3954 Martínez-Cervantes, G. Rodríguez Ruiz, José |
| author_role |
author |
| author2 |
Martínez-Cervantes, G. Rodríguez Ruiz, José |
| author2_role |
author author |
| dc.contributor.none.fl_str_mv |
Escuela Técnica Superior de Ingeniería de Telecomunicación Departamento de Matemática Aplicada Instituto Universitario de Matemática Pura y Aplicada European Regional Development Fund Ministerio de Economía y Competitividad Fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia Agencia Estatal de Investigación Repositorio Institucional de la Universitat Politècnica de València Riunet |
| dc.subject.none.fl_str_mv |
Mackey topology Completeness Norming subspace Mazur property MATEMATICA APLICADA |
| topic |
Mackey topology Completeness Norming subspace Mazur property MATEMATICA APLICADA |
| description |
[EN] We study the class of Banach spaces X such that the locally convex space (X, mu(X,Y)) is complete for every norming and norm-closed subspace Y subset of X*, where mu(X, Y) denotes the Mackey topology on X associated to the dual pair < X, Y >. Such Banach spaces are called fully Mackey complete. We show that fully Mackey completeness is implied by Efremov's property (epsilon) and, on the other hand, it prevents the existence of subspaces isomorphic to l(1)(omega(1)). This extends previous results by Guirao et al. (2017) [9] and Bonet and Cascales (2010) [3]. Further examples of Banach spaces which are not fully Mackey complete are exhibited, like C[0, omega(1)] and the long James space J(omega(1)). Finally, by assuming the Continuum Hypothesis, we construct a Banach space with w*-sequential dual unit ball which is not fully Mackey complete. A key role in our discussion is played by the (at least formally) smaller class of Banach spaces X such that (Y, w*) has the Mazur property for every norming and norm-closed subspace Y subset of X*. (C) 2019 Elsevier Inc. All rights reserved. |
| publishDate |
2019 |
| dc.date.none.fl_str_mv |
2019 2019-10-15 |
| dc.type.none.fl_str_mv |
journal article http://purl.org/coar/resource_type/c_6501 VoR http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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info:eu-repo/semantics/article |
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article |
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https://riunet.upv.es/handle/10251/155855 |
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https://riunet.upv.es/handle/10251/155855 |
| dc.language.none.fl_str_mv |
Inglés eng |
| language_invalid_str_mv |
Inglés |
| language |
eng |
| dc.relation.none.fl_str_mv |
Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016 MTM2017-83262-C2-1-P ANALISIS COMPLEJO Y GEOMETRIA EN ESPACIOS DE BANACH Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016 MTM2017-83262-C2-2-P LA INTERACCION ENTRE GEOMETRIA Y TOPOLOGIA EN ESPACIOS DE BANACH. APLICACIONES. Fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia https://doi.org/10.13039/100007801 19368%2FPI%2F14 Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016 MTM2017-86182-P TEORIA DE CONJUNTOS Y ESPACIOS DE BANACH Ministerio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 MTM2014-54182-P TOPOLOGIA, ANALISIS Y CONJUNTOS Fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia https://doi.org/10.13039/100007801 19275%2FPI%2F14 |
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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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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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