RT Journal Article
T1 Extension of multilinear operators on Banach spaces
A1 Villanueva Díez, Ignacio
A1 Cabello Sánchez, Félix
A1 Garcia, R.
AB This paper considers the problem of extending multilinear forms on a Banach space X to a larger space Y containing it as a closed subspace. For instance, if X is a subspace of Y and X0 ! Y 0 extends linear forms, then the induced Nicodemi operators extend multilinear forms. It is shown that an extension operator X0 ! Y 0 exists if and only if X is locally complemented in Y . Also, these extension operators preserve the symmetry if and only if X is regular. Finally, multlinear characterizations are obtained of some classical Banach space properties (Dunford-Pettis, etc.) related to weak compactness in terms of operators having Z-valued Aron-Berner extensions.
PB Universidad de Extremadura, Departamento de Matemáticas
SN 0213-8743
YR 2001
FD 2001
LK https://hdl.handle.net/20.500.14352/56931
UL https://hdl.handle.net/20.500.14352/56931
LA eng
NO Dirección General de Investigación Científica y Técnica (España)
DS Docta Complutense
RD 15 jun 2025