Open Access
January 2019 Multilinear operators factoring through Hilbert spaces
M. Fernández-Unzueta, S. García-Hernández
Banach J. Math. Anal. 13(1): 234-254 (January 2019). DOI: 10.1215/17358787-2018-0025


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 2 -summing multilinear operators naturally factor through a Hilbert space. We also prove that the class Γ 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 γ which is in duality with Γ .


Download Citation

M. Fernández-Unzueta. S. García-Hernández. "Multilinear operators factoring through Hilbert spaces." Banach J. Math. Anal. 13 (1) 234 - 254, January 2019.


Received: 28 May 2018; Accepted: 30 July 2018; Published: January 2019
First available in Project Euclid: 16 November 2018

zbMATH: 07002040
MathSciNet: MR3892701
Digital Object Identifier: 10.1215/17358787-2018-0025

Primary: 47H60‎
Secondary: 46C05 , 46G25 , 46M05 , 47L22

Keywords: ‎Banach spaces , factoring through a Hilbert space , Lipschitz mappings , multilinear and polynomial mappings , tensor norm

Rights: Copyright © 2019 Tusi Mathematical Research Group

Vol.13 • No. 1 • January 2019
Back to Top