Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4617627 | Journal of Mathematical Analysis and Applications | 2012 | 14 Pages |
Abstract
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 natural operations. We prove that there are exactly six natural symmetric tensor norms for n⩾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.
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