Multilinear operators on C(K,X) spaces
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2004
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Mathematical Institute of the Academy of Sciences of the Czech Republic
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Villanueva Díez, I. «Multilinear Operators on C(K, X) Spaces». Czechoslovak Mathematical Journal, vol. 54, n.o 1, marzo de 2004, pp. 31-54. DOI.org (Crossref), https://doi.org/10.1023/B:CMAJ.0000027245.95757.ee.
Abstract
Given Banach spaces X, Y and a compact Hausdor_ space K, we use polymeasures to give necessary conditions for a multilinear operator from C(K;X) into Y to be completely continuous (resp. unconditionally converging). We deduce necessary and sufficient conditions for X to have the Schur property (resp. to contain no copy of c0), and for K to be scattered. This extends results concerning linear operators.