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Completeness in the Mackey topology

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Completeness in the Mackey topology

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dc.contributor.author Guirao Sánchez, Antonio José es_ES
dc.contributor.author Montesinos Santalucia, Vicente es_ES
dc.date.accessioned 2016-06-13T08:55:43Z
dc.date.available 2016-06-13T08:55:43Z
dc.date.issued 2015-04
dc.identifier.issn 0016-2663
dc.identifier.uri http://hdl.handle.net/10251/65718
dc.description.abstract 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. es_ES
dc.description.sponsorship 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). en_EN
dc.language Inglés es_ES
dc.publisher Springer Verlag es_ES
dc.relation MICINN MTM2008-05396 MTM2011-22417 es_ES
dc.relation FEDER MTM2008-05396 es_ES
dc.relation Fundacion Seneca 08848/PI/08 es_ES
dc.relation Generalitat Valenciana GV/2010/036 es_ES
dc.relation Universitat Politecnica de Valencia PAID-06-09-2829 es_ES
dc.relation.ispartof Functional Analysis and Its Applications es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Mackey-star topology es_ES
dc.subject completeness es_ES
dc.subject local completeness es_ES
dc.subject Banach space es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Completeness in the Mackey topology es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1007/s10688-015-0091-2
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Instituto Universitario de Matemática Pura y Aplicada - Institut Universitari de Matemàtica Pura i Aplicada 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. (2015). Completeness in the Mackey topology. Functional Analysis and Its Applications. 49(2):97-105. doi:10.1007/s10688-015-0091-2 es_ES
dc.description.accrualMethod Senia es_ES
dc.relation.publisherversion http://dx.doi.org/10.1007/s10688-015-0091-2 es_ES
dc.description.upvformatpinicio 97 es_ES
dc.description.upvformatpfin 105 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 49 es_ES
dc.description.issue 2 es_ES
dc.relation.senia 259914 es_ES
dc.identifier.eissn 1573-8485
dc.relation.references J. Bonet and B. Cascales, “Non-complete Mackey topologies on Banach spaces,” Bull. Aust. Math. Soc., 81:3 (2010), 409–413. es_ES
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dc.relation.references J. Diestel, Sequences and Series in Banach Spaces, Graduate Text in Math., vol. 92, Springer-Verlag, New York, 1984. es_ES
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dc.relation.references G. Köthe, Topological Vector Spaces I, Springer-Verlag, New York, 1969. es_ES


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