On the permutative equivalence of squares of unconditional bases

We prove that if the squares of two unconditional bases are equivalent up to a permutation, then the bases themselves are permutatively equivalent. This settles a twenty-five year-old question raised by Casazza and Kalton in [13]. Solving this problem provides a new paradigm to study the uniqueness...

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Autores: Albiac Alesanco, Fernando José, Ansorena, José L.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2022
País:España
Institución:Universidad Pública de Navarra
Repositorio:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
OAI Identifier:oai:academica-e.unavarra.es:2454/44629
Acceso en línea:https://hdl.handle.net/2454/44629
Access Level:acceso abierto
Palabra clave:Banach lattice
Quasi-Banach spaces
Uniqueness of unconditional basis
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spelling On the permutative equivalence of squares of unconditional basesAlbiac Alesanco, Fernando JoséAnsorena, José L.Banach latticeQuasi-Banach spacesUniqueness of unconditional basisWe prove that if the squares of two unconditional bases are equivalent up to a permutation, then the bases themselves are permutatively equivalent. This settles a twenty-five year-old question raised by Casazza and Kalton in [13]. Solving this problem provides a new paradigm to study the uniqueness of unconditional basis in the general framework of quasi-Banach spaces. Multiple examples are given to illustrate how to put in practice this theoretical scheme. Among the main applications of this principle we obtain the uniqueness of unconditional basis up to permutation of finite sums of spaces with this property, as well as the first addition to the scant list of the known Banach spaces with a unique unconditional bases up to permutation since [14].Both authors supported by the Spanish Ministry for Science, Innovation, and Universities, Grant PGC2018-095366-B-I00 for Análisis Vectorial, Multilineal y Approximación. The first-named author also acknowledges the support from Spanish Ministry for Science and Innovation, Grant PID2019-107701GB-I00 for Operators, lattices, and structure of Banach spaces.ElsevierEstatistika, Informatika eta MatematikaInstitute for Advanced Materials and Mathematics - INAMAT2Estadística, Informática y Matemáticas2022info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://hdl.handle.net/2454/44629reponame:Academica-e. Repositorio Institucional de la Universidad Pública de Navarrainstname:Universidad Pública de NavarraInglésinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-095366-B-Iinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-107701GB-I00© 2022 The Author(s). This is an open access article under the CC BY-NC-ND licensehttps://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:academica-e.unavarra.es:2454/446292026-06-17T12:41:47Z
dc.title.none.fl_str_mv On the permutative equivalence of squares of unconditional bases
title On the permutative equivalence of squares of unconditional bases
spellingShingle On the permutative equivalence of squares of unconditional bases
Albiac Alesanco, Fernando José
Banach lattice
Quasi-Banach spaces
Uniqueness of unconditional basis
title_short On the permutative equivalence of squares of unconditional bases
title_full On the permutative equivalence of squares of unconditional bases
title_fullStr On the permutative equivalence of squares of unconditional bases
title_full_unstemmed On the permutative equivalence of squares of unconditional bases
title_sort On the permutative equivalence of squares of unconditional bases
dc.creator.none.fl_str_mv Albiac Alesanco, Fernando José
Ansorena, José L.
author Albiac Alesanco, Fernando José
author_facet Albiac Alesanco, Fernando José
Ansorena, José L.
author_role author
author2 Ansorena, José L.
author2_role author
dc.contributor.none.fl_str_mv Estatistika, Informatika eta Matematika
Institute for Advanced Materials and Mathematics - INAMAT2
Estadística, Informática y Matemáticas
dc.subject.none.fl_str_mv Banach lattice
Quasi-Banach spaces
Uniqueness of unconditional basis
topic Banach lattice
Quasi-Banach spaces
Uniqueness of unconditional basis
description We prove that if the squares of two unconditional bases are equivalent up to a permutation, then the bases themselves are permutatively equivalent. This settles a twenty-five year-old question raised by Casazza and Kalton in [13]. Solving this problem provides a new paradigm to study the uniqueness of unconditional basis in the general framework of quasi-Banach spaces. Multiple examples are given to illustrate how to put in practice this theoretical scheme. Among the main applications of this principle we obtain the uniqueness of unconditional basis up to permutation of finite sums of spaces with this property, as well as the first addition to the scant list of the known Banach spaces with a unique unconditional bases up to permutation since [14].
publishDate 2022
dc.date.none.fl_str_mv 2022
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2454/44629
url https://hdl.handle.net/2454/44629
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-095366-B-I
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-107701GB-I00
dc.rights.none.fl_str_mv © 2022 The Author(s). This is an open access article under the CC BY-NC-ND license
https://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv © 2022 The Author(s). This is an open access article under the CC BY-NC-ND license
https://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
instname:Universidad Pública de Navarra
instname_str Universidad Pública de Navarra
reponame_str Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
collection Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
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