On Cohen weakly nuclear multilinear operators

Abstract

In this paper, we introduce and study a new class of multilinear operators on Banach spaces, called Cohen weakly $p$-nuclear multilinear operators. We establish a Pietsch domination theorem for this new class of multilinear operators. As an application, we show that every Cohen weakly $p$-nuclear multilinear operator is strongly $p$-summing and Cohen strongly $p$-summing.