126289 20241125101151.0 doi 10.1016/j.jmaa.2023.127253 sideral 133614 ART-2023-133614 eng García-Lirola, Luis C. Universidad de Zaragoza (orcid)0000-0001-9211-4475 Lipschitz-free spaces, ultraproducts, and finite representability of metric spaces 2023 Access copy available to the general public Unrestricted We study several properties and applications of the ultrapower of a metric space M. We prove that the Lipschitz-free space is finitely representable in . We also characterize the metric spaces that are finitely Lipschitz representable in a Banach space as those that biLipschitz embed into an ultrapower of the Banach space. Thanks to this link, we obtain that if M is finitely Lipschitz representable in a Banach space X, then is finitely representable in . We apply these results to the study of cotype in Lipschitz-free spaces and the stability of Lipschitz-free spaces and spaces of Lipschitz functions under ultraproducts. info:eu-repo/grantAgreement/ES/AEI-FEDER/ MTM2017-83262-C2-2-P info:eu-repo/grantAgreement/ES/DGA/E48-20R info:eu-repo/grantAgreement/ES/MICINN-AEI-FEDER/PID2021-122126NB-C32 info:eu-repo/semantics/openAccess by http://creativecommons.org/licenses/by/3.0/es/ 1.2 2023 MATHEMATICS 80 / 490 = 0.163 2023 Q1 T1 MATHEMATICS, APPLIED 140 / 332 = 0.422 2023 Q2 T2 0.816 2023 Analysis 2023 Q1 Applied Mathematics 2023 Q2 2.5 2023 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Grelier, Guillaume 2006 015 Universidad de Zaragoza Dpto. Matemáticas Área Análisis Matemático 526, 2 (2023), 127253 [14 pp.] J. math. anal. appl. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 0022-247X 357618 http://zaguan.unizar.es/record/126289/files/texto_completo.pdf Versión publicada 1898303 http://zaguan.unizar.es/record/126289/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:126289 articulos driver 2024-11-22-12:06:58 ARTICLE