The extension theorem for norms on symmetric tensor products of normed spaces

Abstract

It is shown that every s-tensor norm on n-th symmetric tensor products of normed spaces (n fixed) is equivalent to the restriction on symmetric tensor products of a tensor norm (in the sense of Grothendieck) on “full” n-fold tensor products of normed spaces. As α consequence a large part of the isomorphic theory of norms on symmetric tensor products can be deduced from the theory of “full” tensor norms, which usually is easier to handle. Dually, the isomorphic theory of maximal normed ideals of n-homogeneous polynomials can be treated, to a certain extent, through the theory of maximal normed ideals of n-linear functions or mappings .