Addendum to "uniqueness of unconditional basis of infinite direct sums of quasi-Banach spaces"
| 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 | es |
| dc.date.accessioned | 2023-04-17T07:32:08Z | |
| dc.date.available | 2023-04-17T07:32:08Z | |
| dc.date.issued | 2022 | |
| dc.date.updated | 2023-04-17T07:25:49Z | |
| dc.description | Adenda al artículo en https://hdl.handle.net/2454/43360 | es_ES |
| dc.description.abstract | After [Uniqueness of unconditional basis of infinite direct sums of quasi-Banach spaces, Positivity 26 (2022), Paper no. 35] was published, we realized that Theorem 4.2 therein, when combined with work of Casazza and Kalton (Israel J. Math. 103:141-175, 1998) , solves the long-standing problem whether there exists a quasi-Banach space with a unique unconditional basis whose Banach envelope does not have a unique unconditional basis. Here we give examples to prove that the answer is positive. We also use auxiliary results in the aforementioned paper to give a negative answer to the question of Bourgain et al. (Mem Am Math Soc 54:iv+111, 1985)*Problem 1.11 whether the infinite direct sum l(1)(X) of a Banach space X has a unique unconditional basis whenever X does. | en |
| dc.description.sponsorship | Open Access funding provided by Universidad Publica 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. 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 Analisis Vectorial, Multilineal y Aproximacion | en |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.citation | Albiac, F., Ansorena, J.L. Addendum to “uniqueness of unconditional basis of infinite direct sums of quasi-Banach spaces”. Positivity 26, 78 (2022). https://doi.org/10.1007/s11117-022-00942-w | en |
| dc.identifier.doi | 10.1007/s11117-022-00942-w | |
| dc.identifier.issn | 1385-1292 | |
| dc.identifier.uri | https://academica-e.unavarra.es/handle/2454/45133 | |
| dc.language.iso | eng | en |
| dc.publisher | Springer | en |
| dc.relation.ispartof | Positivity (2022) 26:78 | 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/ | |
| 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.publisherversion | https://doi.org/10.1007/s11117-022-00942-w | |
| dc.rights | © The Author(s) 2022. This article is licensed under a Creative Commons Attribution 4.0 International License. | en |
| 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 | Quasi-Banach space | en |
| dc.title | Addendum to "uniqueness of unconditional basis of infinite direct sums of quasi-Banach spaces" | 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 |