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arXiv · 1002.3950

Natural symmetric tensor norms

Daniel Carando·Daniel Galicer
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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.

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Daniel Carando, Daniel Galicer. 2010-02-22. Natural symmetric tensor norms. https://doi.org/10.1016/j.jmaa.2011.09.027

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