Existence of almost greedy bases in mixed-norm sequence and matrix spaces, including besov spaces

We prove that the sequence spaces lp ⊕ lq and the spaces of infinite matrices lp(lq ), lq l(p) and ( ∞ n=1 n lp)lq , which are isomorphic to certain Besov spaces, have an almost greedy basis whenever 0 < p < 1 < q < ∞. More precisely, we custom-build almost greedy bases i...

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Autores: Albiac Alesanco, Fernando José, Ansorena, José L., Bello, Glenier, Wojtaszczyk, Przemyslaw
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2023
País:España
Institución:Universidad San Jorge (USJ)
Repositorio:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
OAI Identifier:oai:academica-e.unavarra.es:2454/46667
Acceso en línea:https://hdl.handle.net/2454/46667
Access Level:acceso abierto
Palabra clave:Almost greedy basis
Conditional basis
Quasi-greedy basis
Subsymmetric basis
Thresholding greedy algorithm
lp-Spaces
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spelling Existence of almost greedy bases in mixed-norm sequence and matrix spaces, including besov spacesAlbiac Alesanco, Fernando JoséAnsorena, José L.Bello, GlenierWojtaszczyk, PrzemyslawAlmost greedy basisConditional basisQuasi-greedy basisSubsymmetric basisThresholding greedy algorithmlp-SpacesWe prove that the sequence spaces lp ⊕ lq and the spaces of infinite matrices lp(lq ), lq l(p) and ( ∞ n=1 n lp)lq , which are isomorphic to certain Besov spaces, have an almost greedy basis whenever 0 < p < 1 < q < ∞. More precisely, we custom-build almost greedy bases in such a way that the Lebesgue parameters grow in a prescribed manner. Our arguments critically depend on the extension of the Dilworth–Kalton– Kutzarova method from Dilworth et al. (Stud Math 159(1):67–101, 2003), which was originally designed for constructing almost greedy bases in Banach spaces, to make it valid for direct sums of mixed-normed spaces with nonlocally convex components. Additionally, we prove that the fundamental functions of all almost greedy bases of these spaces grow as (ml/q )∞ m=l.Open Access funding provided by Universidad Pública de Navarra. 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.SpringerEstadística, Informática y MatemáticasEstatistika, Informatika eta MatematikaInstitute for Advanced Materials and Mathematics - INAMAT2Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa2023info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://hdl.handle.net/2454/46667reponame:Academica-e. Repositorio Institucional de la Universidad Pública de Navarrainstname:Universidad San Jorge (USJ)Inglésinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-107701GB-I00© 2023, The Author(s). This article is licensed under a CreativeCommonsAttribution 4.0 InternationalLicense.https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:academica-e.unavarra.es:2454/466672026-06-17T12:41:47Z
dc.title.none.fl_str_mv Existence of almost greedy bases in mixed-norm sequence and matrix spaces, including besov spaces
title Existence of almost greedy bases in mixed-norm sequence and matrix spaces, including besov spaces
spellingShingle Existence of almost greedy bases in mixed-norm sequence and matrix spaces, including besov spaces
Albiac Alesanco, Fernando José
Almost greedy basis
Conditional basis
Quasi-greedy basis
Subsymmetric basis
Thresholding greedy algorithm
lp-Spaces
title_short Existence of almost greedy bases in mixed-norm sequence and matrix spaces, including besov spaces
title_full Existence of almost greedy bases in mixed-norm sequence and matrix spaces, including besov spaces
title_fullStr Existence of almost greedy bases in mixed-norm sequence and matrix spaces, including besov spaces
title_full_unstemmed Existence of almost greedy bases in mixed-norm sequence and matrix spaces, including besov spaces
title_sort Existence of almost greedy bases in mixed-norm sequence and matrix spaces, including besov spaces
dc.creator.none.fl_str_mv Albiac Alesanco, Fernando José
Ansorena, José L.
Bello, Glenier
Wojtaszczyk, Przemyslaw
author Albiac Alesanco, Fernando José
author_facet Albiac Alesanco, Fernando José
Ansorena, José L.
Bello, Glenier
Wojtaszczyk, Przemyslaw
author_role author
author2 Ansorena, José L.
Bello, Glenier
Wojtaszczyk, Przemyslaw
author2_role author
author
author
dc.contributor.none.fl_str_mv Estadística, Informática y Matemáticas
Estatistika, Informatika eta Matematika
Institute for Advanced Materials and Mathematics - INAMAT2
Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
dc.subject.none.fl_str_mv Almost greedy basis
Conditional basis
Quasi-greedy basis
Subsymmetric basis
Thresholding greedy algorithm
lp-Spaces
topic Almost greedy basis
Conditional basis
Quasi-greedy basis
Subsymmetric basis
Thresholding greedy algorithm
lp-Spaces
description We prove that the sequence spaces lp ⊕ lq and the spaces of infinite matrices lp(lq ), lq l(p) and ( ∞ n=1 n lp)lq , which are isomorphic to certain Besov spaces, have an almost greedy basis whenever 0 < p < 1 < q < ∞. More precisely, we custom-build almost greedy bases in such a way that the Lebesgue parameters grow in a prescribed manner. Our arguments critically depend on the extension of the Dilworth–Kalton– Kutzarova method from Dilworth et al. (Stud Math 159(1):67–101, 2003), which was originally designed for constructing almost greedy bases in Banach spaces, to make it valid for direct sums of mixed-normed spaces with nonlocally convex components. Additionally, we prove that the fundamental functions of all almost greedy bases of these spaces grow as (ml/q )∞ m=l.
publishDate 2023
dc.date.none.fl_str_mv 2023
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/2454/46667
url https://hdl.handle.net/2454/46667
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/PID2019-107701GB-I00
dc.rights.none.fl_str_mv https://creativecommons.org/licenses/by/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
instname:Universidad San Jorge (USJ)
instname_str Universidad San Jorge (USJ)
reponame_str Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
collection Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
repository.name.fl_str_mv
repository.mail.fl_str_mv
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