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

#### 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.
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2006
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/55866