$(p,q)$-Dominated Multilinear Operators and Laprest\'e tensor norms
| Autor: | Fernández-Unzueta, M., García-Hernández, Samuel |
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| Rok vydání: | 2018 |
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| Druh dokumentu: | Working Paper |
| Popis: | We introduce a notion of $(p,q)$-dominated multilinear operators which stems from the geometrical approach provided by $\Sigma$-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 Laprest\'e tensor norm. We also prove that they verify a generalization of the Pietsch's Domination Theorem and Kwapie\'n's Factorization Theorem. Also, we study the collection $\mathcal{D}_{p,q}$ of all $(p,q)$-dominated multilinear operators showing that $\mathcal{D}_{p,q}$ has a maximal ideal demeanor and that the Laprest\'e norm has a finitely generated behavior. Comment: 22 Pages |
| Databáze: | arXiv |
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