On norm-attainment in (symmetric) tensor products

Dantas, Sheldon ; García-Lirola, Luis C. (Universidad de Zaragoza) ; Jung, Mingu ; Zoca, Abraham Rueda

Resumen: In this paper, we introduce a concept of norm-attainment in the projective symmetric tensor product of a Banach space X, which turns out to be naturally related to the classical norm-attainment of N -homogeneous polynomials on X. Due to this relation, we can prove that there exist symmetric tensors that do not attain their norms, which allows us to study the problem of when the set of norm-attaining elements in is dense. We show that the set of all normattaining symmetric tensors is dense in for a large set of Banach spaces such as Lp-spaces, isometric L1-predual spaces or Banach spaces with monotone Schauder basis, among others. Next, we prove that if X* satisfies the Radon-Nikodým and approximation properties, then the set of all norm-attaining symmetric tensors in is dense. From these techniques, we can present new examples of Banach spaces X and Y such that the set of all norm-attaining tensors in the projective tensor product is dense, answering positively an open question from the paper [10].

Idioma: Inglés

DOI: 10.2989/16073606.2022.2032862

Año: 2022

Publicado en: QUAESTIONES MATHEMATICAE (2022), 1-17
ISSN: 1607-3606

Factor impacto JCR: 0.7 (2022)

Categ. JCR: MATHEMATICS rank: 203 / 329 = 0.617 (2022) - Q3 - T2

Factor impacto CITESCORE: 1.9 - Mathematics (Q2)

Factor impacto SCIMAGO: 0.427 - Mathematics (miscellaneous) (Q2)

Financiación: info:eu-repo/grantAgreement/ES/AEI-FEDER/ MTM2017-83262-C2-2-P

Tipo y forma: Article (PostPrint)

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