Uniqueness of unconditional basis of infinite direct sums of quasi-Banach spaces

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dc.contributor.authorAlbiac Alesanco, Fernando José
dc.contributor.authorAnsorena, José L.
dc.contributor.departmentEstadística, Informática y Matemáticases_ES
dc.contributor.departmentEstatistika, Informatika eta Matematikaeu
dc.date.accessioned2022-07-19T11:29:25Z
dc.date.available2022-07-19T11:29:25Z
dc.date.issued2022
dc.date.updated2022-07-01T11:38:18Z
dc.descriptionAddendum en https://hdl.handle.net/2454/45133
dc.description.abstractThis paper is devoted to providing a unifying approach to the study of the uniqueness of unconditional bases, up to equivalence and permutation, of infinite direct sums of quasi-Banach spaces. Our new approach to this type of problem permits to show that a wide class of vector-valued sequence spaces have a unique unconditional basis up to a permutation. In particular, solving a problem from Albiac and Leránoz (J Math Anal Appl 374(2):394-401, 2011. https://doi.org/10.1016/j.jmaa.2010.09.048) we show that if X is quasi-Banach space with a strongly absolute unconditional basis then the infinite direct sum -1(X) has a unique unconditional basis up to a permutation, even without knowing whether X has a unique unconditional basis or not. Applications to the uniqueness of unconditional structure of infinite direct sums of non-locally convex Orlicz and Lorentz sequence spaces, among other classical spaces, are also obtained as a by-product of our work.en
dc.description.sponsorshipF. Albiac acknowledges the support of the Spanish Ministry for Science and Innovation under Grant PID2019-107701GB-I00 for Operators, lattices, and structure of Banach spaces. F. Albiac and J. L. Ansorena acknowledge the support of the Spanish Ministry for Science, Innovation, and Universities under Grant PGC2018-095366-B-I00 for Análisis Vectorial, Multilineal y Aproximación.en
dc.format.mimetypeapplication/pdfen
dc.identifier.citationAlbiac-Alesanco, F.; Ansorena, J. L. (2022). Uniqueness of unconditional basis of infinite direct sums of quasi-Banach spaces. Positivity: An International Journal Devoted to the Theory and Applications of Positivity in Analysis. 26,en
dc.identifier.doi10.1007/s11117-022-00905-1
dc.identifier.issn1385-1292
dc.identifier.urihttps://academica-e.unavarra.es/handle/2454/43360
dc.language.isoengen
dc.publisherKluwer Academic Publishersen
dc.relation.ispartofPositivity: an International Journal Devoted to the Theory and Applications of Positivity in Analysis, 2022, vol. 26en
dc.relation.projectIDinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-107701GB-I00/ES/
dc.relation.projectIDinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-095366-B-I00/ES/
dc.relation.publisherversionhttps://doi.org/10.1007/s11117-022-00905-1
dc.rights©The Author(s) 2022. This article is licensed under a Creative Commons Attribution 4.0 International Licenseen
dc.rights.accessRightsinfo:eu-repo/semantics/openAccess
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectBanach latticeen
dc.subjectEquivalence of basesen
dc.subjectQuasi-Banach spaceen
dc.subjectUnconditional basisen
dc.subjectUniquenessen
dc.titleUniqueness of unconditional basis of infinite direct sums of quasi-Banach spacesen
dc.typeinfo:eu-repo/semantics/article
dc.type.versioninfo:eu-repo/semantics/publishedVersion
dspace.entity.typePublication
relation.isAuthorOfPublication3a702006-6ba1-41ba-93bf-ea9fee1de239
relation.isAuthorOfPublication.latestForDiscovery3a702006-6ba1-41ba-93bf-ea9fee1de239

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