Completeness in the Mackey topology

Bonet and Cascales [Non-complete Mackey topologies on Banach spaces, Bulletin of the Australian Mathematical Society, 81, 3 (2010), 409-413], answering a question of M. Kunze and W. Arendt, gave an example of a norming norm-closed subspace N of the dual of a Banach space X such that mu(X, N) is not...

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Autores: Guirao Sánchez, Antonio José|||0000-0002-1031-3954, Montesinos Santalucia, Vicente
Tipo de recurso: artículo
Fecha de publicación:2015
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:10251/65718
Acceso en línea:https://riunet.upv.es/handle/10251/65718
Access Level:acceso abierto
Palabra clave:Mackey-star topology
completeness
local completeness
Banach space
MATEMATICA APLICADA
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spelling Completeness in the Mackey topologyGuirao Sánchez, Antonio José|||0000-0002-1031-3954Montesinos Santalucia, VicenteMackey-star topologycompletenesslocal completenessBanach spaceMATEMATICA APLICADABonet and Cascales [Non-complete Mackey topologies on Banach spaces, Bulletin of the Australian Mathematical Society, 81, 3 (2010), 409-413], answering a question of M. Kunze and W. Arendt, gave an example of a norming norm-closed subspace N of the dual of a Banach space X such that mu(X, N) is not complete,where mu(X, N) denotes the Mackey topology associated with the dual pair aEuroX, NaEuro parts per thousand. We prove in this note that we can decide on the completeness or incompleteness of topologies of this form in a quite general context, thus providing large classes of counterexamples to the aforesaid question. Moreover, our examples use subspaces N of X* that contain a predual P of X (if exists), showing that the phenomenon of noncompleteness that Kunze and Arendt were looking for is not only relatively common but illustrated by "well-located" subspaces of the dual. We discuss also the situation for a typical Banach space without a predual-the space c (0)-and for the James space J.The first author is supported in part by MICINN and FEDER (project no. MTM2008-05396), by Fundacion Seneca (project no. 08848/PI/08), by Generalitat Valenciana (GV/2010/036), and by Universitat Politecnica de Valencia (project no. PAID-06-09-2829). The second author is supported in part by MICINN project no. MTM2011-22417, by Generalitat Valenciana (GV/2010/036), and by Universidad Politecnica de Valencia (project no. PAID-06-09-2829).Springer VerlagEscuela Técnica Superior de Ingeniería de TelecomunicaciónDepartamento de Matemática AplicadaInstituto Universitario de Matemática Pura y AplicadaMinisterio de Ciencia e InnovaciónGeneralitat ValencianaUniversitat Politècnica de ValènciaFundación Séneca-Agencia de Ciencia y Tecnología de la Región de MurciaRepositorio Institucional de la Universitat Politècnica de València Riunet20152015-04-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/65718reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengMinisterio de Ciencia e Innovación http://dx.doi.org/10.13039/501100004837 MTM2008-05396 LA INTERACCION ENTRE TEORIA DE LA MEDIDA, TOPOLOGIA Y ANALISIS FUNCIONALFundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia https://doi.org/10.13039/100007801 08848%2FPI%2F08 Medida, Topología, Análisis funcional y sus aplicaciones en finanzasGeneralitat Valenciana https://doi.org/10.13039/501100003359 GV%2F2010%2F036Universitat Politècnica de València https://doi.org/10.13039/501100004233 PAID-06-09-2829Ministerio de Ciencia e Innovación http://dx.doi.org/10.13039/501100004837 MTM2011-22417 ESPACIOS Y ALGEBRAS DE FUNCIONES DIFERENCIABLESopen 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:10251/657182026-06-13T07:49:27Z
dc.title.none.fl_str_mv Completeness in the Mackey topology
title Completeness in the Mackey topology
spellingShingle Completeness in the Mackey topology
Guirao Sánchez, Antonio José|||0000-0002-1031-3954
Mackey-star topology
completeness
local completeness
Banach space
MATEMATICA APLICADA
title_short Completeness in the Mackey topology
title_full Completeness in the Mackey topology
title_fullStr Completeness in the Mackey topology
title_full_unstemmed Completeness in the Mackey topology
title_sort Completeness in the Mackey topology
dc.creator.none.fl_str_mv Guirao Sánchez, Antonio José|||0000-0002-1031-3954
Montesinos Santalucia, Vicente
author Guirao Sánchez, Antonio José|||0000-0002-1031-3954
author_facet Guirao Sánchez, Antonio José|||0000-0002-1031-3954
Montesinos Santalucia, Vicente
author_role author
author2 Montesinos Santalucia, Vicente
author2_role 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
Ministerio de Ciencia e Innovación
Generalitat Valenciana
Universitat Politècnica de València
Fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Mackey-star topology
completeness
local completeness
Banach space
MATEMATICA APLICADA
topic Mackey-star topology
completeness
local completeness
Banach space
MATEMATICA APLICADA
description Bonet and Cascales [Non-complete Mackey topologies on Banach spaces, Bulletin of the Australian Mathematical Society, 81, 3 (2010), 409-413], answering a question of M. Kunze and W. Arendt, gave an example of a norming norm-closed subspace N of the dual of a Banach space X such that mu(X, N) is not complete,where mu(X, N) denotes the Mackey topology associated with the dual pair aEuroX, NaEuro parts per thousand. We prove in this note that we can decide on the completeness or incompleteness of topologies of this form in a quite general context, thus providing large classes of counterexamples to the aforesaid question. Moreover, our examples use subspaces N of X* that contain a predual P of X (if exists), showing that the phenomenon of noncompleteness that Kunze and Arendt were looking for is not only relatively common but illustrated by "well-located" subspaces of the dual. We discuss also the situation for a typical Banach space without a predual-the space c (0)-and for the James space J.
publishDate 2015
dc.date.none.fl_str_mv 2015
2015-04-01
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/10251/65718
url https://riunet.upv.es/handle/10251/65718
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Ciencia e Innovación http://dx.doi.org/10.13039/501100004837 MTM2008-05396 LA INTERACCION ENTRE TEORIA DE LA MEDIDA, TOPOLOGIA Y ANALISIS FUNCIONAL
Fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia https://doi.org/10.13039/100007801 08848%2FPI%2F08 Medida, Topología, Análisis funcional y sus aplicaciones en finanzas
Generalitat Valenciana https://doi.org/10.13039/501100003359 GV%2F2010%2F036
Universitat Politècnica de València https://doi.org/10.13039/501100004233 PAID-06-09-2829
Ministerio de Ciencia e Innovación http://dx.doi.org/10.13039/501100004837 MTM2011-22417 ESPACIOS Y ALGEBRAS DE FUNCIONES DIFERENCIABLES
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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