International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 1, Pages 69-76
doi:10.1155/S0161171200000715

Random trilinear forms and the Schur multiplication of tensors

Ibrahim Almasri,1 Jinlu Li,2 and Andrew Tonge3

1College of Engineering and Technology, The West Bank, Hebron, Palestinian Authority
2Mathematics Department, Shawnee State University, Portsmouth 45662, OH, USA
3Department of Mathematics and Computer Science, Kent State University, Kent 44242, OH, USA

Received 27 November 1996; Revised 3 March 1998

Copyright © 2000 Ibrahim Almasri et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.