Non-superreflexivity of Garling sequence spaces and applications to the existence of special types of conditional bases

Albiac Alesanco, Fernando José; Ansorena, José L.; Dilworth, S. J.; Kutzarova, Denka

doi:10.4064/sm180910-1-2

dc.creator	Albiac Alesanco, Fernando José	es_ES
dc.creator	Ansorena, José L.	es_ES
dc.creator	Dilworth, S. J.	es_ES
dc.creator	Kutzarova, Denka	es_ES
dc.date.accessioned	2021-03-17T12:50:15Z
dc.date.available	2021-03-17T12:50:15Z
dc.date.issued	2020
dc.identifier.issn	1730-6337 (Electronic)
dc.identifier.uri	https://hdl.handle.net/2454/39431
dc.description.abstract	We settle in the negative the problem of the superreflexivity of Garling sequence spaces by showing that they contain a complemented subspace isomorphic to a non-superreflexive mixed-norm sequence space. As a by-product, we give applications to the study of conditional Schauder bases and conditional almost greedy bases in this new class of Banach spaces.	en
dc.description.sponsorship	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 Analisis Vectorial, multilineal, y aproximacion. F. Albiac was also supported by the grant MTM2016-76808-P (MINECO, Spain) for Operators, lattices, and structure of Banach spaces. S. J. Dilworth was supported by the National Science Foundation under Grant Number DMS-1361461. Denka Kutzarova acknowledges the support from Simmons Foundation Collaborative Grant Number 636954. S. J. Dilworth and D. Kutzarova were supported by the Workshop in Analysis and Probability at Texas A&M University in 2017.	en
dc.format.extent	14 p.
dc.format.mimetype	application/pdf	en
dc.language.iso	eng	en
dc.publisher	Instytut Matematyczny	en
dc.relation.ispartof	Studia Mathematica, 2020, 251(3), 277-288	en
dc.rights	© Instytut Matematyczny PAN, 2020	en
dc.subject	Subsymmetric basis	en
dc.subject	Garling sequence spaces	en
dc.subject	Superreflexivity	en
dc.subject	Besov spaces	en
dc.subject	Conditional bases	en
dc.subject	Conditionality constants	en
dc.subject	Almost greedy bases	en
dc.title	Non-superreflexivity of Garling sequence spaces and applications to the existence of special types of conditional bases	en
dc.type	info:eu-repo/semantics/article	en
dc.type	Artículo / Artikulua	es
dc.contributor.department	Estadística, Informática y Matemáticas	es_ES
dc.contributor.department	Estatistika, Informatika eta Matematika	eu
dc.contributor.department	Institute for Advanced Materials and Mathematics - INAMAT2	es_ES
dc.rights.accessRights	info:eu-repo/semantics/openAccess	en
dc.rights.accessRights	Acceso abierto / Sarbide irekia	es
dc.identifier.doi	10.4064/sm180910-1-2
dc.relation.projectID	info:eu-repo/grantAgreement/ES/1PE/MTM2016-76808-P	en
dc.relation.publisherversion	https://doi.org/10.4064/sm180910-1-2
dc.type.version	info:eu-repo/semantics/acceptedVersion	en
dc.type.version	Versión aceptada / Onetsi den bertsioa	es

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