The inclusion theorem for multiple summing operators

Volume 165 / 2004

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


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.


  • David Pérez-GarcíaÁrea Matemática Aplicada
    ESCET, Universidad Rey Juan Carlos
    C/ Tulipán s/n
    28933 Mostoles (Madrid), Spain

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