Natural symmetric tensor norms
Copyright policy )Natural symmetric tensor norms
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
- National Scientific and Technical Research Council Argentina
- University of Buenos Aires Argentina
46M05, 46H05, 47A80, polynomials on Banach spaces, Natural Tensor Norms, Applied Mathematics, Polinomial Ideals, Symmetric Tensor Products, Polynomials in Banach spaces, Functional Analysis (math.FA), Mathematics - Functional Analysis, (Spaces of) multilinear mappings, polynomials, symmetric tensor products, FOS: Mathematics, https://purl.org/becyt/ford/1.1, natural tensor norms, Tensor products in functional analysis, Banach algebras, https://purl.org/becyt/ford/1, Natural tensor norms, Symmetric tensor products, Analysis
46M05, 46H05, 47A80, polynomials on Banach spaces, Natural Tensor Norms, Applied Mathematics, Polinomial Ideals, Symmetric Tensor Products, Polynomials in Banach spaces, Functional Analysis (math.FA), Mathematics - Functional Analysis, (Spaces of) multilinear mappings, polynomials, symmetric tensor products, FOS: Mathematics, https://purl.org/becyt/ford/1.1, natural tensor norms, Tensor products in functional analysis, Banach algebras, https://purl.org/becyt/ford/1, Natural tensor norms, Symmetric tensor products, Analysis
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