Villanueva, Ignacio and Cabello Sánchez, Félix and Garcia, R. (2001) Extension of multilinear operators on Banach spaces. Extracta Mathematicae, 15 (2). pp. 291334. ISSN 02138743

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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 (DunfordPettis, etc.) related to weak compactness in terms of operators having Zvalued AronBerner extensions.
Item Type:  Article 

Uncontrolled Keywords:  DunfordPettis; Extending multilinear forms; Nicodemi operators; Extension operator; Locally complemented; Multlinear characterizations; Banach space properties; Weak compactness; Zvalued AronBerner 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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