Factorization theorems for some new classes of multilinear operators

Abstract

[EN] Two new classes of summing multilinear operators, factorable (q,p)-summing operators and (r;p,q)-summing operators are studied. These classes are described in terms of factorization. It is shown that operators in the first (resp., the second) class admit the factorization through the injective tensor product of Banach spaces (resp., through some Banach lattices). Applications in different contexts related to Grothendieck Theorem and Fourier integral bilinear operators are shown. Motivated by Pisier¿s Theorem on factorization of (q,1)-summing operators from C(K)-spaces through Lorentz spaces Lq,1 on some probability Borel measure spaces, we prove two variants of Pisier¿s Theorem for bilinear operators on the product of C(K)-spaces. We also prove bilinear versions of Mityagin¿Pe¿czy¿ski and Kislyakov Theorems.