Uniqueness of unconditional basis of Hp(T) ⊕ 2 and Hp(T) ⊕ T (2) for 0 < p < 1

Albiac Alesanco, Fernando José; Ansorena, José L.; Wojtaszczyk, Przemyslaw

Publication:
Uniqueness of unconditional basis of Hp(T) ⊕ 2 and Hp(T) ⊕ T (2) for 0 < p < 1

dc.contributor.author	Albiac Alesanco, Fernando José
dc.contributor.author	Ansorena, José L.	es_ES
dc.contributor.author	Wojtaszczyk, Przemyslaw	es_ES
dc.contributor.department	Estatistika, Informatika eta Matematika	eu
dc.contributor.department	Institute for Advanced Materials and Mathematics - INAMAT2	en
dc.contributor.department	Estadística, Informática y Matemáticas	es_ES
dc.date.accessioned	2022-11-30T08:09:38Z
dc.date.available	2022-11-30T08:09:38Z
dc.date.issued	2022
dc.date.updated	2022-11-18T12:22:19Z
dc.description.abstract	Our goal in this paper is to advance the state of the art of the topic of uniqueness of unconditional basis. To that end we establish general conditions on a pair (X, Y) formed by a quasi-Banach space X and a Banach space Y which guarantee that every unconditional basis of their direct sum X ⊕ Y splits into unconditional bases of each summand. As application of our methods we obtain that, among others, the spaces Hp(Td) ⊕ T (2) and Hp(Td) ⊕ 2, for p ∈ (0, 1) and d ∈ N, have a unique unconditional basis (up to equivalence and permutation).	en
dc.description.sponsorship	F. 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. P. Wojtaszczyk was supported by National Science Centre, Poland grant UMO-2016/21/B/ST1/00241.	en
dc.format.mimetype	application/pdf	en
dc.identifier.citation	Albiac, F., Ansorena, J. L., & Wojtaszczyk, P. (2022). Uniqueness of unconditional basis of H p (T) ⊕ ℓ 2 and H p ⊕(T) T for(2) 0 < p < 1. Journal of Functional Analysis, 283(7), 109597.	en
dc.identifier.doi	10.1016/j.jfa.2022.109597
dc.identifier.issn	0022-1236
dc.identifier.uri	https://academica-e.unavarra.es/handle/2454/44396
dc.language.iso	eng	en
dc.publisher	Elsevier	en
dc.relation.ispartof	Journal of Functional Analysis 283 (2022) 109597	en
dc.relation.projectID	info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-107701GB-I00/ES/	en
dc.relation.projectID	info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-095366-B-I00/ES/	en
dc.relation.publisherversion	https://doi.org/10.1016/j.jfa.2022.109597
dc.rights	© 2022 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license	en
dc.rights.accessRights	Acceso abierto / Sarbide irekia	es
dc.rights.accessRights	info:eu-repo/semantics/openAccess	en
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subject	Hardy spaces	en
dc.subject	Lattice techniques in quasi-Banach spaces	en
dc.subject	Tsirelson space	en
dc.subject	Uniqueness of unconditional basis	en
dc.title	Uniqueness of unconditional basis of Hp(T) ⊕ 2 and Hp(T) ⊕ T (2) for 0 < p < 1	en
dc.type	Artículo / Artikulua	es
dc.type	info:eu-repo/semantics/article	en
dc.type.version	Versión publicada / Argitaratu den bertsioa	es
dc.type.version	info:eu-repo/semantics/publishedVersion	en
dspace.entity.type	Publication
relation.isAuthorOfPublication	3a702006-6ba1-41ba-93bf-ea9fee1de239
relation.isAuthorOfPublication.latestForDiscovery	3a702006-6ba1-41ba-93bf-ea9fee1de239