doi:10.1007/s43037-024-00400-7engGarcía-Lirola, Luis C.Guerrero-Viu, JuanRueda Zoca, AbrahamProjective tensor products where every element is norm-attainingART-2025-143119In 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.2025http://zaguan.unizar.es/record/15140010.1007/s43037-024-00400-7http://zaguan.unizar.es/record/151400oai:zaguan.unizar.es:151400info:eu-repo/grantAgreement/ES/DGA/E48-23Rinfo:eu-repo/grantAgreement/ES/MICINN-AEI-FEDER/PID2021-122126NB-C31info:eu-repo/grantAgreement/ES/MICINN/PID2022-137294NB-I00Banach Journal of Mathematical Analysis 19, 2 (2025), 20 pp.byhttps://creativecommons.org/licenses/by/4.0/deed.esinfo:eu-repo/semantics/openAccess