The inclusion theorem for multiple summing operators
We prove that, for $1\le p\le q<2$, each multiple $p$-summing multilinear operator between Banach spaces is also $q$-summing. We also give an improvement of this result for an image space of cotype $2$. As a consequence, we obtain a characterization of Hilbert–Schmidt multilinear operators similar to the linear one given by A. Pe/lczyński in 1967. We also give a multilinear generalization of Grothendieck's Theorem for GT spaces.