Inclusion theorems for Cohen strongly summing multilinear operators

Abstract

In this paper we investigate connections between the class of Cohen strongly summing multilinear operators and other classes of multilinear mappings, such as multiple summing and strongly summing mappings (in the sense of Dimant). As a consequence of our results, we show that if $Y$ is a $\mathcal{L}_{p^{\ast }}$-space and $X_{1},...,X_{m}$ are $\mathcal{L}_{p}$-spaces ($1<p<\infty $ and $1/p+1/p^{\ast }=1)$, then every multiple $p^{\ast }$-summing $m$-linear operator is strongly $p^{\ast }$-summing.