(p,q)-Dominated Multilinear Operators and Lapresté tensor norms

2018/08/14 by Fernández-Unzueta, M., García-Hernández, Samuel
#46G25 #46M05 (Secondary) #47H60 (Primary) 47B10 #47L22 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1808.04842

Abstract

We introduce a notion of (p,q)-dominated multilinear operators which stems from the geometrical approach provided by Σ-operators. We prove that (p,q)-dominated multilinear operators can be characterized in terms of their behavior on finite sequences and in terms of their relation with a Lapresté tensor norm. We also prove that they verify a generalization of the Pietsch's Domination Theorem and Kwapień's Factorization Theorem. Also, we study the collection D_p,q of all (p,q)-dominated multilinear operators showing that D_p,q has a maximal ideal demeanor and that the Lapresté norm has a finitely generated behavior.

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