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 Kwapień, from the linear to the multilinear setting. We prove that Hilbert–Schmidt and Lipschitz -summing multilinear operators naturally factor through a Hilbert space. We also prove that the class 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 which is in duality with .
"Multilinear operators factoring through Hilbert spaces." Banach J. Math. Anal. 13 (1) 234 - 254, January 2019. https://doi.org/10.1215/17358787-2018-0025