The inclusion theorem for multiple summing operators
Studia Mathematica, Tome 165 (2004) no. 3, pp. 275-290
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We prove that, for $1\le p\le q2$, 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.
Keywords:
prove each multiple p summing multilinear operator between banach spaces q summing improvement result image space cotype consequence obtain characterization hilbert schmidt multilinear operators similar linear given lczy ski multilinear generalization grothendiecks theorem spaces
Affiliations des auteurs :
David Pérez-García 1
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author = {David P\'erez-Garc{\'\i}a},
title = {The inclusion theorem for multiple summing operators},
journal = {Studia Mathematica},
pages = {275--290},
publisher = {mathdoc},
volume = {165},
number = {3},
year = {2004},
doi = {10.4064/sm165-3-5},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm165-3-5/}
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David Pérez-García. The inclusion theorem for multiple summing operators. Studia Mathematica, Tome 165 (2004) no. 3, pp. 275-290. doi: 10.4064/sm165-3-5
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