Geodesic
Multilinear operators on $C(K,X)$ spaces
Czechoslovak Mathematical Journal, Tome 54 (2004) no. 1, pp. 31-54
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Given Banach spaces~ $X$, $Y$ and a compact Hausdorff 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~ $c_0$), and for~ $K$ to be scattered. This extends results concerning linear operators.
Given Banach spaces~ $X$, $Y$ and a compact Hausdorff 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~ $c_0$), and for~ $K$ to be scattered. This extends results concerning linear operators.
Classification : 46B25, 46G10, 46G25, 47B07, 47H60
Keywords: completely continuous; unconditionally converging; multilinear operators; $C(K, X)$ spaces 
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Villanueva, Ignacio. Multilinear operators on $C(K,X)$ spaces. Czechoslovak Mathematical Journal, Tome 54 (2004) no. 1, pp. 31-54. http://geodesic.mathdoc.fr/item/CMJ_2004_54_1_a2/

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