Geodesic
Multilinear operators on $C(K,X)$ spaces
Czechoslovak Mathematical Journal, Tome 54 (2004) no. 1, pp. 31-54.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 
@article{CMJ_2004__54_1_a2,
     author = {Villanueva, Ignacio},
     title = {Multilinear operators on $C(K,X)$ spaces},
     journal = {Czechoslovak Mathematical Journal},
     pages = {31--54},
     publisher = {mathdoc},
     volume = {54},
     number = {1},
     year = {2004},
     mrnumber = {2040217},
     zbl = {1050.46032},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2004__54_1_a2/}
}
TY  - JOUR
AU  - Villanueva, Ignacio
TI  - Multilinear operators on $C(K,X)$ spaces
JO  - Czechoslovak Mathematical Journal
PY  - 2004
SP  - 31
EP  - 54
VL  - 54
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMJ_2004__54_1_a2/
LA  - en
ID  - CMJ_2004__54_1_a2
ER  - 
%0 Journal Article
%A Villanueva, Ignacio
%T Multilinear operators on $C(K,X)$ spaces
%J Czechoslovak Mathematical Journal
%D 2004
%P 31-54
%V 54
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMJ_2004__54_1_a2/
%G en
%F CMJ_2004__54_1_a2
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/