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dc.contributor.author | Hájek, Petr | es_ES |
dc.contributor.author | Quilis-Sandemetrio, Andres | es_ES |
dc.date.accessioned | 2023-07-13T18:02:33Z | |
dc.date.available | 2023-07-13T18:02:33Z | |
dc.date.issued | 2022-07-01 | es_ES |
dc.identifier.issn | 0022-1236 | es_ES |
dc.identifier.uri | http://hdl.handle.net/10251/194941 | |
dc.description.abstract | [EN] In the present paper we introduce and study the Lipschitz retractional structure of metric spaces. This topic was motivated by the analogous projectional structure of Banach spaces, a topic that has been thoroughly investigated. The more general metric setting fits well with the currently active theory of Lipschitz free spaces and spaces of Lipschitz functions. Among our applications we show that the Lipschitz free space F(X) is a Plichko space whenever X is a Plichko Banach space. Our main results include two examples of metric spaces. The first one M contains two points {0, 1} such that no separable subset of M containing these points is a Lipschitz retract of M. The second example fails the analogous property for arbitrary infinite density. Finally, we introduce the metric version of the concept of locally complemented Banach subspace, and prove some metric analogues to the linear theory. | es_ES |
dc.description.sponsorship | This research was supported by CAAS CZ.02.1.01/0.0/0.0/16-019/0000778,bytheprojectSGS21/056/OHK3/1T/13andbyPAID-01-19. The authors also wish to thank the anonymous referee for their insightful remarks. | es_ES |
dc.language | Inglés | es_ES |
dc.publisher | Elsevier | es_ES |
dc.relation.ispartof | Journal of Functional Analysis | es_ES |
dc.rights | Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) | es_ES |
dc.subject | Lipschitz retractions | es_ES |
dc.subject | Complementation properties of Banach spaces | es_ES |
dc.title | Lipschitz retractions and complementation properties in Banach spaces | es_ES |
dc.type | Artículo | es_ES |
dc.identifier.doi | 10.1016/j.jfa.2022.109494 | es_ES |
dc.relation.projectID | info:eu-repo/grantAgreement/UPV-VIN//PAID-01-19-32//Espacios Lipschitz-free asociado a espacios de Banach./ | es_ES |
dc.relation.projectID | info:eu-repo/grantAgreement/FEDER//CZ.02.1.01%2F0.0%2F0.0%2F16-019%2F0000778/ | es_ES |
dc.relation.projectID | info:eu-repo/grantAgreement/MEYS//SGS21%2F056%2FOHK3%2F1T%2F13/ | es_ES |
dc.rights.accessRights | Abierto | es_ES |
dc.description.bibliographicCitation | Hájek, P.; Quilis-Sandemetrio, A. (2022). Lipschitz retractions and complementation properties in Banach spaces. Journal of Functional Analysis. 283(1):1-35. https://doi.org/10.1016/j.jfa.2022.109494 | es_ES |
dc.description.accrualMethod | S | es_ES |
dc.relation.publisherversion | https://doi.org/10.1016/j.jfa.2022.109494 | es_ES |
dc.description.upvformatpinicio | 1 | es_ES |
dc.description.upvformatpfin | 35 | es_ES |
dc.type.version | info:eu-repo/semantics/publishedVersion | es_ES |
dc.description.volume | 283 | es_ES |
dc.description.issue | 1 | es_ES |
dc.relation.pasarela | S\462618 | es_ES |
dc.contributor.funder | European Regional Development Fund | es_ES |
dc.contributor.funder | UNIVERSIDAD POLITECNICA DE VALENCIA | es_ES |
dc.contributor.funder | Ministry of Education, Youth and Sport of the Czech Republic | es_ES |