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A note on Mackey topologies on Banach spaces

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A note on Mackey topologies on Banach spaces

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dc.contributor.author Guirao Sánchez, Antonio José es_ES
dc.contributor.author Montesinos Santalucia, Vicente es_ES
dc.contributor.author Zizler, Vaclav es_ES
dc.date.accessioned 2018-09-17T07:10:18Z
dc.date.available 2018-09-17T07:10:18Z
dc.date.issued 2017 es_ES
dc.identifier.issn 0022-247X es_ES
dc.identifier.uri http://hdl.handle.net/10251/107361
dc.description.abstract [EN] There is a maybe unexpected connection between three apparently unrelated notions concerning a given w*-dense subspace Y of the dual X* of a Banach space X: (i) The norming character of Y, (ii) the fact that (Y, w*) has the Mazur property, and (iii) the completeness of the Mackey topology mu(X, Y), i.e., the topology on X of the uniform convergence on the family of all absolutely convex w*-compact subsets of Y. To clarify these connections is the purpose of this note. The starting point was a question raised by M. Kunze and W. Arendt and the answer provided by J. Bonet and B. Cascales. We fully characterize mu(X, Y)-completeness or its failure in the case of Banach spaces X with a w*-angelic dual unit ball in particular, separable Banach spaces or, more generally, wealdy compactly generated ones-by using the norming or, alternatively, the Mazur character of Y. We characterize the class of spaces where the original Kunze-Arendt question has always a positive answer. Some other applications are also provided. (C) 2016 Elsevier Inc. All rights reserved. es_ES
dc.description.sponsorship Supported in part by MICINN (Project MTM2014-57838-C2-2-P). es_ES
dc.language Inglés es_ES
dc.publisher Elsevier es_ES
dc.relation.ispartof Journal of Mathematical Analysis and Applications es_ES
dc.rights Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) es_ES
dc.subject Banach space es_ES
dc.subject Mackey topology es_ES
dc.subject Completeness es_ES
dc.subject Norming subspace es_ES
dc.subject Mazur space es_ES
dc.subject Weak compactness es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title A note on Mackey topologies on Banach spaces es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1016/j.jmaa.2016.08.030 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/f SéNeCa//19368%2FPI%2F14/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/MINECO//MTM2014-57838-C2-1-P/ES/LA INTERACCION ENTRE GEOMETRIA Y TOPOLOGIA EN ESPACIOS DE BANACH. APLICACIONES/ es_ES
dc.rights.accessRights Abierto es_ES
dc.date.embargoEndDate 2019-01-01 es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.description.bibliographicCitation Guirao Sánchez, AJ.; Montesinos Santalucia, V.; Zizler, V. (2017). A note on Mackey topologies on Banach spaces. Journal of Mathematical Analysis and Applications. 445(1):944-952. https://doi.org/10.1016/j.jmaa.2016.08.030 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion http://doi.org/10.1016/j.jmaa.2016.08.030 es_ES
dc.description.upvformatpinicio 944 es_ES
dc.description.upvformatpfin 952 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 445 es_ES
dc.description.issue 1 es_ES
dc.relation.pasarela S\327182 es_ES
dc.contributor.funder Ministerio de Economía y Competitividad es_ES
dc.contributor.funder Fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia es_ES


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