Lipschitz free spaces isomorphic to their infinite sums and geometric applications
| dc.contributor.author | Albiac Alesanco, Fernando José | |
| dc.contributor.author | Ansorena, José L. | |
| dc.contributor.author | Cúth, Marek | |
| dc.contributor.author | Doucha, Michal | |
| 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 | 2022-01-24T11:40:05Z | |
| dc.date.available | 2022-01-24T11:40:05Z | |
| dc.date.issued | 2021 | |
| dc.description.abstract | We find general conditions under which Lipschitz-free spaces over metric spaces are isomorphic to their infinite direct _1-sum and exhibit several applications. As examples of such applications we have that Lipschitz-free spaces over balls and spheres of the same finite dimensions are isomorphic, that the Lipschitz-free space over Zd is isomorphic to its _1-sum, or that the Lipschitz-free space over any snowflake of a doubling metric space is isomorphic to l1. Moreover, following new ideas of Bruè et al. from [J. Funct. Anal. 280 (2021), pp. 108868, 21] we provide an elementary self-contained proof that Lipschitz-free spaces over doubling metric spaces are complemented in Lipschitz-free spaces over their superspaces and they have BAP. Everything, including the results about doubling metric spaces, is explored in the more comprehensive setting of p-Banach spaces, which allows us to appreciate the similarities and differences of the theory between the cases p < 1 and p = 1. | en |
| dc.description.sponsorship | The first author acknowledges the support of the Spanish Ministry for Science and Innovation under Grant PID2019-107701GB-I00 for Operators, lattices, and structure of Banach spaces and the support of the Spanish Ministry for Science, Innovation, and Universities under Grant PGC2018-095366-B-I00 for Análisis Vectorial, Multilineal y Aproximación. The second author acknowledges the support of the Spanish Ministry for Science, Innovation, and Universities under Grant PGC2018-095366-B-I00 for Análisis Vectorial, Multilineal y Aproximación. The third author was supported by Charles University Research program No. UNCE/SCI/023. The fourth author was supported by the GACˇR project 19-05271Y and RVO: 67985840. | en |
| dc.format.extent | 40 p. | |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.doi | 10.1090/tran/8444 | |
| dc.identifier.issn | 0002-9947 | |
| dc.identifier.uri | https://academica-e.unavarra.es/handle/2454/41919 | |
| dc.language.iso | eng | en |
| dc.publisher | American Mathematical Society | |
| dc.relation.ispartof | Transactions of the American Mathematical Society, 374 (10), 7281-7312 | |
| 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/10.1090/tran/8444 | |
| dc.rights | © 2021 American Mathematical Society. Creative Commons Atribución-NoComercial-SinDerivadas 4.0 Internacional | en |
| dc.rights.accessRights | info:eu-repo/semantics/openAccess | |
| dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/4.0/ | |
| dc.subject | Arens-Eells space | en |
| dc.subject | Lipschitz free p-space | en |
| dc.subject | Lipschitz free space | en |
| dc.subject | Quasi-Banach space | en |
| dc.subject | Transportation cost space | en |
| dc.title | Lipschitz free spaces isomorphic to their infinite sums and geometric applications | 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 |