On certain subspaces of p for 0 < p ≤ 1 and their applications to conditional quasi-greedy bases in p-Banach spaces
| dc.contributor.author | Albiac Alesanco, Fernando José | |
| dc.contributor.author | Ansorena, José L. | |
| 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 | 2021-03-17T12:50:14Z | |
| dc.date.available | 2021-10-01T23:00:10Z | |
| dc.date.issued | 2021 | |
| dc.description.abstract | We construct for each 0<p≤1 an infinite collection of subspaces of ℓp that extend the example of Lindenstrauss (Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 12, 539–542, 1964) of a subspace of ℓ1 with no unconditional basis. The structure of this new class of p-Banach spaces is analyzed and some applications to the general theory of Lp-spaces for 0<p<1 are provided. The introduction of these spaces serves the purpose to develop the theory of conditional quasi-greedy bases in p-Banach spaces for p<1. Among the topics we consider are the existence of infinitely many conditional quasi-greedy bases in the spaces ℓp for p≤1 and the careful examination of the conditionality constants of the 'natural basis' of these spaces. | en |
| dc.description.sponsorship | F. Albiac acknowledges the support of the Spanish Ministry for Economy and Competitivity under Grant MTM2016-76808-P as well as the Spanish Ministry for Science and Innovation under Grant PID2019-1077701GB-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.embargo.lift | 2021-10-01 | |
| dc.embargo.terms | 2021-10-01 | |
| dc.format.extent | 38 p. | |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.doi | 10.1007/s00208-020-02069-3 | |
| dc.identifier.issn | 1432-1807 (Electronic) | |
| dc.identifier.uri | https://academica-e.unavarra.es/handle/2454/39429 | |
| dc.language.iso | eng | en |
| dc.publisher | Springer | en |
| dc.relation.ispartof | Mathematische Annalen, 2021, 379, 465–502 | en |
| dc.relation.projectID | info:eu-repo/grantAgreement/ES/1PE/MTM2016-76808-P/ | |
| dc.relation.publisherversion | https://doi.org/10.1007/s00208-020-02069-3 | |
| dc.rights | © Springer-Verlag GmbH Germany, part of Springer Nature 2020 | en |
| dc.rights.accessRights | info:eu-repo/semantics/openAccess | |
| dc.subject | Subspaces of ℓp | en |
| dc.subject | Banach spaces | en |
| dc.title | On certain subspaces of p for 0 < p ≤ 1 and their applications to conditional quasi-greedy bases in p-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 |