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

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

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

dc.contributor.author	Albiac Alesanco, Fernando José
dc.contributor.author	Ansorena, José L.
dc.contributor.author	Bello, Glenier
dc.contributor.author	Wojtaszczyk, Przemyslaw
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	en
dc.contributor.funder	Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa	es
dc.date.accessioned	2023-10-30T12:32:55Z
dc.date.available	2023-10-30T12:32:55Z
dc.date.issued	2023
dc.date.updated	2023-10-30T11:49:21Z
dc.description.abstract	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.	en
dc.description.sponsorship	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.	en
dc.format.mimetype	application/pdf	en
dc.identifier.citation	Albiac, F., Ansorena, J. L., Bello, G., & Wojtaszczyk, P. (2023). Existence of almost greedy bases in mixed-norm sequence and matrix spaces, including besov spaces. Constructive Approximation. https://doi.org/10.1007/s00365-023-09662-0	en
dc.identifier.doi	10.1007/s00365-023-09662-0
dc.identifier.issn	0176-4276
dc.identifier.uri	https://academica-e.unavarra.es/handle/2454/46667
dc.language.iso	eng	en
dc.publisher	Springer	en
dc.relation.ispartof	Constructive Approximation (2023), 1-31	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.publisherversion	https://doi.org/10.1007/s00365-023-09662-0
dc.rights	© 2023, The Author(s). This article is licensed under a CreativeCommonsAttribution 4.0 InternationalLicense.	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/4.0/
dc.subject	Almost greedy basis	en
dc.subject	Conditional basis	en
dc.subject	Quasi-greedy basis	en
dc.subject	Subsymmetric basis	en
dc.subject	Thresholding greedy algorithm	en
dc.subject	lp-Spaces	en
dc.title	Existence of almost greedy bases in mixed-norm sequence and matrix spaces, including besov spaces	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