(p,q)-dominated multilinear operators and Lapresté tensor norms

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 ten...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2019-02, Vol.470 (2), p.982-1003
Main Authors: Fernández-Unzueta, Maite, García-Hernández, Samuel
Format: Article
Language:English
Subjects:
Dominated operators
Ideals of multilinear mappings
Multilinear and polynomial mappings
Tensor products
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Summary: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 satisfy a generalization of the Pietsch's Domination Theorem and Kwapień's Factorization Theorem. Also, we study the collection Dp,q of all (p,q)-dominated multilinear operators showing that Dp,q has a maximal ideal demeanor and that the Lapresté norm has a finitely generated behavior.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2018.10.044