123842 20240319081006.0 doi 10.2989/16073606.2022.2032862 sideral 131335 ART-2022-131335 eng Dantas, Sheldon On norm-attainment in (symmetric) tensor products 2022 Access copy available to the general public Unrestricted 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]. info:eu-repo/grantAgreement/ES/AEI-FEDER/ MTM2017-83262-C2-2-P info:eu-repo/semantics/openAccess by-nc http://creativecommons.org/licenses/by-nc/3.0/es/ 0.7 2022 MATHEMATICS 203 / 329 = 0.617 2022 Q3 T2 0.427 2022 Mathematics (miscellaneous) 2022 Q2 1.9 2022 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion García-Lirola, Luis C. Universidad de Zaragoza (orcid)0000-0001-9211-4475 Jung, Mingu Zoca, Abraham Rueda 2006 015 Universidad de Zaragoza Dpto. Matemáticas Área Análisis Matemático (2022), 1-17 Quaest. math. (Grahamst., Print) QUAESTIONES MATHEMATICAE 1607-3606 751789 http://zaguan.unizar.es/record/123842/files/texto_completo.pdf Postprint 810159 http://zaguan.unizar.es/record/123842/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:123842 articulos driver 2024-03-18-14:38:59 ARTICLE