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arXiv · 1805.09748

Multilinear Operators Factoring through Hilbert Spaces

Maite Fernández-Unzueta·Samuel García-Hernández
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Abstract

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 $\Gamma$.

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Maite Fernández-Unzueta, Samuel García-Hernández. 2018-05-24. Multilinear Operators Factoring through Hilbert Spaces. https://doi.org/10.1215/17358787-2018-0025

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