Lipschitz-free spaces, ultraproducts, and finite representability of metric spaces

García-Lirola, Luis C. (Universidad de Zaragoza) ; Grelier, Guillaume

Resumen: 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.

Idioma: Inglés

DOI: 10.1016/j.jmaa.2023.127253

Año: 2023

Publicado en: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 526, 2 (2023), 127253 [14 pp.]
ISSN: 0022-247X

Factor impacto JCR: 1.2 (2023)

Categ. JCR: MATHEMATICS rank: 80 / 490 = 0.163 (2023) - Q1 - T1
Categ. JCR: MATHEMATICS, APPLIED rank: 140 / 332 = 0.422 (2023) - Q2 - T2

Factor impacto CITESCORE: 2.5 - Analysis (Q2) - Applied Mathematics (Q2)

Factor impacto SCIMAGO: 0.816 - Analysis (Q1) - Applied Mathematics (Q2)

Financiación: info:eu-repo/grantAgreement/ES/AEI-FEDER/ MTM2017-83262-C2-2-P
Financiación: info:eu-repo/grantAgreement/ES/DGA/E48-20R
Financiación: info:eu-repo/grantAgreement/ES/MICINN-AEI-FEDER/PID2021-122126NB-C32

Tipo y forma: Article (Published version)

Área (Departamento): Área Análisis Matemático (Dpto. Matemáticas)