Random trilinear forms and the Schur multiplication of tensors
Ibrahim Almasri,1Jinlu Li,2and Andrew Tonge3
Received27 Nov 1996
Revised03 Mar 1998
Abstract
We obtain estimates for the distribution of the norm of the random
trilinear form A:ℓrM×ℓpN×ℓqK→ℂ, defined by A(ei,ej,ek)=aijk, where the aijk's are uniformly bounded, independent, mean zero
random variables. As an application, we make progress on the
problem when ℓr⊗⌣ℓp⊗⌣ℓq is a Banach algebra under the Schur multiplication.