CONICET | Buscador de Institutos y Recursos Humanos

In the spirit of the work of Grothendieck, we introduce and study natural symmetric n-fold tensor norms. These are norms obtained from the projective norm by some extit{natural} operations. We prove that there are exactly six natural symmetric tensor norms for $nge 3$, a noteworthy difference with the 2-fold case in which there are four. We also describe the polynomial ideals associated to these natural symmetric tensor norms. Using a symmetric version of a result of Carne, we establish which natural symmetric tensor norms preserve the Banach algebra structure.