Natural symmetric tensor norms

Details Natural symmetric tensor norms Natural symmetric tensor norms

2010-02-22

arxiv.org/abs/1002.3950v4

J. Math. Anal. Appl. 387 (2012) 568-581

Mathematics

Functional Analysis

22 pages

Scientific paper

10.1016/j.jmaa.2011.09.027

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.

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