# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## The inclusion theorem for multiple summing operators

### Tom 165 / 2004

Studia Mathematica 165 (2004), 275-290 MSC: Primary 47H60; Secondary 46B25, 46C99. DOI: 10.4064/sm165-3-5

#### Streszczenie

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.