1. Multilinear operators on $C(K,X)$ spaces
- Creator:
- Villanueva, Ignacio
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- completely continuous, unconditionally converging, multilinear operators, and $C(K,X)$ spaces
- Language:
- English
- Description:
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public