000123842 001__ 123842 000123842 005__ 20240319081006.0 000123842 0247_ $$2doi$$a10.2989/16073606.2022.2032862 000123842 0248_ $$2sideral$$a131335 000123842 037__ $$aART-2022-131335 000123842 041__ $$aeng 000123842 100__ $$aDantas, Sheldon 000123842 245__ $$aOn norm-attainment in (symmetric) tensor products 000123842 260__ $$c2022 000123842 5060_ $$aAccess copy available to the general public$$fUnrestricted 000123842 5203_ $$aIn 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]. 000123842 536__ $$9info:eu-repo/grantAgreement/ES/AEI-FEDER/ MTM2017-83262-C2-2-P 000123842 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc$$uhttp://creativecommons.org/licenses/by-nc/3.0/es/ 000123842 590__ $$a0.7$$b2022 000123842 592__ $$a0.427$$b2022 000123842 591__ $$aMATHEMATICS$$b203 / 329 = 0.617$$c2022$$dQ3$$eT2 000123842 593__ $$aMathematics (miscellaneous)$$c2022$$dQ2 000123842 594__ $$a1.9$$b2022 000123842 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000123842 700__ $$0(orcid)0000-0001-9211-4475$$aGarcía-Lirola, Luis C.$$uUniversidad de Zaragoza 000123842 700__ $$aJung, Mingu 000123842 700__ $$aZoca, Abraham Rueda 000123842 7102_ $$12006$$2015$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Análisis Matemático 000123842 773__ $$g(2022), 1-17$$pQuaest. math. (Grahamst., Print)$$tQUAESTIONES MATHEMATICAE$$x1607-3606 000123842 8564_ $$s751789$$uhttps://zaguan.unizar.es/record/123842/files/texto_completo.pdf$$yPostprint 000123842 8564_ $$s810159$$uhttps://zaguan.unizar.es/record/123842/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000123842 909CO $$ooai:zaguan.unizar.es:123842$$particulos$$pdriver 000123842 951__ $$a2024-03-18-14:38:59 000123842 980__ $$aARTICLE