The uniqueness of unconditional basis of the 2-convexified Tsirelson space, revisited
| dc.contributor.author | Albiac Alesanco, Fernando José | |
| dc.contributor.author | Ansorena, José L. | |
| 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 | |
| dc.date.accessioned | 2025-03-05T16:33:30Z | |
| dc.date.available | 2025-03-05T16:33:30Z | |
| dc.date.issued | 2024-10-13 | |
| dc.date.updated | 2025-03-05T15:08:04Z | |
| dc.description.abstract | One of the hallmarks in the study of the classification of Banach spaces with a unique (normalized) unconditional basis was the unexpected result by Bourgain, Casazza, Lindenstrauss, and Tzafriri from their 1985 Memoir that the 2-convexified Tsirelson space T(2) had that property (up to equivalence and permutation). Indeed, on one hand, finding a “pathological” space (i.e., not built out as a direct sum of the only three classical sequence spaces with a unique unconditional basis) shattered the hopeful optimism of attaining a satisfactory description of all Banach spaces which enjoy that important structural feature. On the other hand it encouraged furthering a research topic that had received relatively little attention until then. After forty years, the advances on the subject have shed light onto the underlying patterns shared by those spaces with a unique unconditional bases belonging to the same class, which has led to reproving the original theorems with fewer technicalities. Our motivation in this note is to revisit the aforementioned result on the uniqueness of unconditional basis of T(2) from the current state-of-art of the subject and to fill in some details that we missed from the original proof. | en |
| dc.description.sponsorship | The authors acknowledge the support of the Spanish Ministry for Science and Innovation under Grant PID2022-138342NB-I00 for Functional Analysis Techniques in Approximation Theory and Applications. Open Access funding provided by Universidad Pública de Navarra. | |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.citation | Albiac, F., Ansorena, J. L. (2024) The uniqueness of unconditional basis of the 2-convexified Tsirelson space, revisited. Banach Journal of Mathematical Analysis, 18(4), 1-15. https://doi.org/10.1007/s43037-024-00386-2. | |
| dc.identifier.doi | 10.1007/s43037-024-00386-2 | |
| dc.identifier.issn | 2662-2033 | |
| dc.identifier.uri | https://academica-e.unavarra.es/handle/2454/53672 | |
| dc.language.iso | eng | |
| dc.publisher | Springer | |
| dc.relation.ispartof | Banach Journal of Mathematical Analysis, (2024) 18:79 | |
| dc.relation.projectID | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2022-138342NB-I00/ES/ | |
| dc.relation.publisherversion | https://doi.org/10.1007/s43037-024-00386-2 | |
| dc.rights | © The Author(s) 2024. This article is licensed under a Creative Commons Attribution 4.0 International License. | |
| dc.rights.accessRights | info:eu-repo/semantics/openAccess | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.subject | Uniqueness of unconditional basis | en |
| dc.subject | Banach lattices | en |
| dc.subject | Tsirelson space | en |
| dc.subject | Sequence spaces | en |
| dc.title | The uniqueness of unconditional basis of the 2-convexified Tsirelson space, revisited | en |
| dc.type | info:eu-repo/semantics/article | |
| dc.type.version | info:eu-repo/semantics/publishedVersion | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 3a702006-6ba1-41ba-93bf-ea9fee1de239 | |
| relation.isAuthorOfPublication.latestForDiscovery | 3a702006-6ba1-41ba-93bf-ea9fee1de239 |