Greedy approximation for biorthogonal systems in quasi-Banach spaces
| dc.contributor.author | Albiac Alesanco, Fernando José | |
| dc.contributor.author | Ansorena, José L. | |
| dc.contributor.author | Berná, Pablo M. | |
| dc.contributor.author | Wojtaszczyk, Przemyslaw | |
| 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 | 2022-01-26T08:35:10Z | |
| dc.date.available | 2022-04-29T23:00:12Z | |
| dc.date.issued | 2021 | |
| dc.description.abstract | The general problem addressed in this work is the development of a systematic study of the thresholding greedy algorithm for general biorthogonal systems in quasi-Banach spaces from a functional-analytic point of view. If (Formula Presented) is a biorthogonal system in X then for each x ∈ X we have a formal expansion (Formula Presented). The thresholding greedy algorithm (with threshold ε > 0) applied to x is formally defined as (Formula Presented). The properties of this operator give rise to the different classes of greedy-type bases. We revisit the concepts of greedy, quasi-greedy, and almost greedy bases in this comprehensive framework and provide the (non-trivial) extensions of the corresponding characterizations of those types of bases. As a by-product of our work, new properties arise, and the relations among them are carefully discussed. | 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 Grant PGC2018-095366-B-I00 for Análisis Vectorial, Multilineal y Aplicaciones. P. M. Berná acknowledges the support of the Spanish Ministry for Economy and Competitivity Grants MTM-2016-76566-P and PID2019-105599GB-100 (Agencia Estatal de Investigación). P. M. Berná was also supported by Grant 20906/PI/18 from Fundación Séneca (Región de Murcia, Spain). P. Wojtaszczyk was partially supported by National Science Centre, Poland, grant UMO-2016/21/B/ST1/00241. This work was supported by EPSRC grant number EP/R014604/1. | en |
| dc.embargo.lift | 2022-04-29 | |
| dc.embargo.terms | 2022-04-29 | |
| dc.format.extent | 104 p. | |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.doi | 10.4064/dm817-11-2020 | |
| dc.identifier.issn | 0012-3862 | |
| dc.identifier.uri | https://academica-e.unavarra.es/handle/2454/41955 | |
| dc.language.iso | eng | en |
| dc.publisher | Instytut Matematyczny | |
| dc.relation.ispartof | Dissertationes Mathematicae, 560, (2021), 1-88 | en |
| dc.relation.projectID | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-105599GB-I00/ES/ | |
| dc.relation.projectID | info:eu-repo/grantAgreement/ES/1PE/MTM2016-76566-P/ | |
| 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/ | |
| dc.relation.projectID | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-107701GB-I00/ES/ | |
| dc.relation.publisherversion | https://doi.org/10.4064/dm817-11-2020 | |
| dc.rights | © Instytut Matematyczny PAN, Warszawa 2021. | en |
| dc.rights.accessRights | info:eu-repo/semantics/openAccess | |
| dc.subject | Almost greedy | en |
| dc.subject | Democratic basis | en |
| dc.subject | Greedy basis | en |
| dc.subject | Quasi-Banach spaces | en |
| dc.subject | Quasi-greedy basis | en |
| dc.subject | Unconditional basis | en |
| dc.title | Greedy approximation for biorthogonal systems in quasi-Banach spaces | en |
| dc.type | info:eu-repo/semantics/article | |
| dc.type.version | info:eu-repo/semantics/acceptedVersion | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 3a702006-6ba1-41ba-93bf-ea9fee1de239 | |
| relation.isAuthorOfPublication.latestForDiscovery | 3a702006-6ba1-41ba-93bf-ea9fee1de239 |