Projective tensor products where every element is norm-attaining

García-Lirola, Luis C. (Universidad de Zaragoza) ; Guerrero-Viu, Juan (Universidad de Zaragoza) ; Rueda Zoca, Abraham

Resumen: In this paper we analyse when every element of attains its projective norm. We prove that this is the case if X is the dual of a subspace of a predual of an space and Y is 1-complemented in its bidual under approximation property assumptions. This result allows us to provide some new examples where X is a Lipschitz-free space. We also prove that the set of norm-attaining elements is dense in if, for instance, and Y is any Banach space, or if X has the metric -property and Y is a dual space with the RNP.

Idioma: Inglés

DOI: 10.1007/s43037-024-00400-7

Año: 2025

Publicado en: Banach Journal of Mathematical Analysis 19, 2 (2025), 20 pp.
ISSN: 2662-2033

Financiación: info:eu-repo/grantAgreement/ES/DGA/E48-23R
Financiación: info:eu-repo/grantAgreement/ES/MICINN-AEI-FEDER/PID2021-122126NB-C31
Financiación: info:eu-repo/grantAgreement/ES/MICINN/PID2022-137294NB-I00

Tipo y forma: Article (Published version)

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