We prove that, for 1 ≤ p ≤ 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. Pełczyński in 1967. We also give a multilinear generalization of Grothendieck's Theorem for GT spaces.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm165-3-5,
author = {David P\'erez-Garc\'\i a},
title = {The inclusion theorem for multiple summing operators},
journal = {Studia Mathematica},
volume = {162},
year = {2004},
pages = {275-290},
zbl = {1064.47057},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm165-3-5}
}
David Pérez-García. The inclusion theorem for multiple summing operators. Studia Mathematica, Tome 162 (2004) pp. 275-290. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm165-3-5/