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
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.
|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|
|Deposited On:||15 Nov 2010 13:28|
|Last Modified:||11 Dec 2013 18:38|