Multilinear Operators Factoring through Hilbert Spaces
| Autor: | Fernández-Unzueta, Maite, García-Hernández, Samuel |
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| Rok vydání: | 2018 |
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| Zdroj: | Banach J. Math. Anal. 13, no. 1 (2019), 234-254 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1215/17358787-2018-0025 |
| Popis: | We characterize those bounded multilinear operators that factor through a Hilbert space in terms of its behavior in finite sequences. This extends a result, essentially due to S. Kwapie\'{n}, from the linear to the multilinear setting. We prove that Hilbert-Schmidt and Lipschitz $2$-summing multilinear operators naturally factor through a Hilbert space. It is also proved that the class $\Gamma$ of all multilinear operators that factor through a Hilbert space is a maximal multi-ideal; moreover, we give an explicit formulation of a finitely generated tensor norm $\gamma$ which is in duality with $\Gamma$. Comment: 19 pages |
| Databáze: | arXiv |
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