Natural symmetric tensor norms

Abstract

In the spirit of the work of Grothendieck, we introduce and study natural symmetric n-fold tensor norms. We prove that there are exactly six natural symmetric tensor norms for $n\ge 3$, 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 Banach algebras.

22 pages

References in corpus (1)

• Extending polynomials in maximal and minimal ideals

Cited by in corpus (4)

• Holomorphic Functions and polynomial ideals on Banach spaces
• The symmetric Radon-Nikodým property for tensor norms
• Unconditionality in tensor products and ideals of polynomials, multilinear forms and operators
• Five basic lemmas for symmetric tensor products of normed spaces