Counterexamples in isometric theory of symmetric and greedy bases
| dc.contributor.author | Albiac Alesanco, Fernando José | |
| dc.contributor.author | Ansorena, José L. | |
| dc.contributor.author | Blasco, Óscar | |
| dc.contributor.author | Chu, Hùng Việt | |
| dc.contributor.author | Oikhberg, Timur | |
| 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 | 2024-05-07T19:04:49Z | |
| dc.date.available | 2024-05-07T19:04:49Z | |
| dc.date.issued | 2024 | |
| dc.date.updated | 2024-05-07T18:45:40Z | |
| dc.description.abstract | We continue the study initiated in Albiac and Wojtaszczyk (2006) of properties related to greedy bases in the case when the constants involved are sharp, i.e., in the case when they are equal to 1. Our main goal here is to provide an example of a Banach space with a basis that satisfies Property (A) but fails to be 1-suppression unconditional, thus settling Problem 4.4 from Albiac and Ansorena (2017). In particular, our construction demonstrates that bases with Property (A) need not be 1-greedy even with the additional assumption that they are unconditional and symmetric. We also exhibit a finite-dimensional counterpart of this example, and show that, at least in the finite-dimensional setting, Property (A) does not pass to the dual. As a by-product of our arguments, we prove that a symmetric basis is unconditional if and only if it is total, thus generalizing the well-known result that symmetric Schauder bases are unconditional. | en |
| dc.description.sponsorship | The research of F. Albiac, J.L. Ansorena, and Ó. Blasco was funded by the Spanish Ministry for Science and Innovation under Grant PID2022-138342NB-I00 for Functional analysis methods in approximation theory and applications. F. Albiac also acknowledges the support of the Spanish Ministry for Science and Innovation under Grant PID2019-107701GB-I00 for Operators, lattices, and structure of Banach spaces. The University of Illinois partially supported the work of H. V. Chu and T. Oikhberg via Campus Research Board award 23026. Open Access funding provided by Universidad Pública de Navarra. | en |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.citation | Albiac, F., Ansorena, J. L., Blasco, Ó., Chu, H. V., Oikhberg, T. (2024) Counterexamples in isometric theory of symmetric and greedy bases. Journal of Approximation Theory, 297, 1-20. https://doi.org/10.1016/j.jat.2023.105970. | en |
| dc.identifier.doi | 10.1016/j.jat.2023.105970 | |
| dc.identifier.issn | 0021-9045 | |
| dc.identifier.uri | https://academica-e.unavarra.es/handle/2454/48077 | |
| dc.language.iso | eng | en |
| dc.publisher | Elsevier | en |
| dc.relation.ispartof | Journal of Approximation Theory 297, 2024,105970 | en |
| 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.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/10.1016/j.jat.2023.105970 | |
| dc.rights | © 2023 The Author(s). This is an open access article under the CC BY license. | en |
| dc.rights.accessRights | info:eu-repo/semantics/openAccess | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.subject | Greedy basis | en |
| dc.subject | Property (A) | en |
| dc.subject | Suppression unconditional basis | en |
| dc.subject | Symmetric basis | en |
| dc.subject | Thresholding greedy algorithm | en |
| dc.title | Counterexamples in isometric theory of symmetric and greedy bases | 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 |