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Extension of multilinear operators on Banach spaces

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

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Abstract

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

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