Show simple item record

dc.creatorAlbiac Alesanco, Fernando Josées_ES
dc.creatorAnsorena, José L.es_ES
dc.creatorWojtaszczyk, Przemyslawes_ES
dc.date.accessioned2019-08-26T11:13:29Z
dc.date.available2019-08-26T11:13:29Z
dc.date.issued2019
dc.identifier.issn1432-0940
dc.identifier.urihttps://hdl.handle.net/2454/34670
dc.descriptionThis is a post-peer-review, pre-copyedit version of an article published in Constr Approx (2019) 49:103–122. The final authenticated version is available online at: https://doi.org/10.1007/s00365-017-9399-xen
dc.description.abstractFor a conditional quasi-greedy basis B in a Banach space, the associated conditionality constants km[B] verify the estimate km[B]=O(logm). Answering a question raised by Temlyakov, Yang, and Ye, several authors have studied whether this bound can be improved when we consider quasi-greedy bases in some special class of spaces. It is known that every quasi-greedy basis in a superreflexive Banach space verifies km[B]=O((logm)1-E) for some 0<E<1, and this is optimal. Our first goal in this paper will be to fill the gap between the general case and the superreflexive case and investigate the growth of the conditionality constants in nonsuperreflexive spaces. Roughly speaking, the moral will be that we can guarantee optimal bounds only for quasi-greedy bases in superreflexive spaces. We prove that if a Banach space X is not superreflexive, then there is a quasi-greedy basis B in a Banach space Y finitely representable in X with km[B]approximate to logm. As a consequence, we obtain that for every 2<q<, there is a Banach space X of type 2 and cotype q possessing a quasi-greedy basis B with km[B]approximate to logm. We also tackle the corresponding problem for Schauder bases and show that if a space is nonsuperreflexive, then it possesses a basic sequence B with km[B]approximate to m.en
dc.description.sponsorshipF. Albiac and J. L. Ansorena were partially supported by the Spanish Research Grant Analisis Vectorial, Multilineal y Aplicaciones, Reference Number MTM2014-53009-P. F. Albiac also acknowledges the support of Spanish Research Grant Operators, lattices, and structure of Banach spaces, with reference MTM2016-76808-P. P. Wojtaszczyk was partially supported by National Science Centre, Poland Grant UMO-2016/21/B/ST1/00241.en
dc.format.extent21 p.
dc.format.mimetypeapplication/pdfen
dc.language.isoengen
dc.publisherSpringeren
dc.relation.ispartofConstructive Approximation, 49 (1), 103-122en
dc.rights© Springer Science+Business Media, LLC 2017en
dc.subjectThresholding greedy algorithmen
dc.subjectConditional basisen
dc.subjectConditionality constantsen
dc.subjectQuasi-greedy basisen
dc.subjectTypeen
dc.subjectCotypeen
dc.subjectReflexivityen
dc.subjectSuperreflexivityen
dc.subjectSuper propertyen
dc.subjectFinite representabilityen
dc.subjectBanach spacesen
dc.titleConditional quasi-greedy bases in non-superreflexive Banach spacesen
dc.typeinfo:eu-repo/semantics/articleen
dc.typeArtículo / Artikuluaes
dc.contributor.departmentUniversidad Pública de Navarra. Departamento de Estadística, Informática y Matemáticases_ES
dc.contributor.departmentNafarroako Unibertsitate Publikoa. Estatistika, Informatika eta Matematika Sailaeu
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen
dc.rights.accessRightsAcceso abierto / Sarbide irekiaes
dc.identifier.doi10.1007/s00365-017-9399-x
dc.relation.projectIDinfo:eu-repo/grantAgreement/ES/1PE/MTM2014-53009-Pen
dc.relation.projectIDinfo:eu-repo/grantAgreement/ES/1PE/MTM2016-76808-Pen
dc.relation.publisherversionhttps://doi.org/10.1007/s00365-017-9399-x
dc.type.versioninfo:eu-repo/semantics/acceptedVersionen
dc.type.versionVersión aceptada / Onetsi den bertsioaes


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record