Extension of multilinear operators on Banach spaces



Downloads per month over past year

Villanueva, Ignacio and Cabello Sánchez, Félix and Garcia, R. (2001) Extension of multilinear operators on Banach spaces. Extracta Mathematicae, 15 (2). pp. 291-334. ISSN 0213-8743

[thumbnail of 2000Extensionofmultilinearoperators.pdf]

Official URL: http://www.unex.es/extracta/extracta.html


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.

Item Type:Article
Uncontrolled Keywords:Dunford-Pettis; Extending multilinear forms; Nicodemi operators; Extension operator; Locally complemented; Multlinear characterizations; Banach space properties; Weak compactness; Z-valued Aron-Berner extensions
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:11524
Deposited On:15 Nov 2010 12:28
Last Modified:06 Feb 2014 09:05

Origin of downloads

Repository Staff Only: item control page