We prove that several definitions of integral multilinear mappings given in the literature are equivalent. We show that what we call S-factorizable multilinear mappings are integral, but that the converse is not true (contrary to earlier claims). Using S-factorizable polynomials we give characterizations of ${\mathscr L}_\infty$-spaces, Asplund spaces, spaces not containing $\ell_1$, and spaces with the compact range property. Some of these characterizations seem to be new even for linear operators.
Integral and S-factorizable multilinear mappings
CILIA, Raffaela Giovanna;
2006-01-01
Abstract
We prove that several definitions of integral multilinear mappings given in the literature are equivalent. We show that what we call S-factorizable multilinear mappings are integral, but that the converse is not true (contrary to earlier claims). Using S-factorizable polynomials we give characterizations of ${\mathscr L}_\infty$-spaces, Asplund spaces, spaces not containing $\ell_1$, and spaces with the compact range property. Some of these characterizations seem to be new even for linear operators.File in questo prodotto:
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