Extension of multilinear operators on Banach spaces (Q2708479)

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 \(X'\to Y'\) extends linear forms, then the induced Nicodemi operators extend multilinear forms. It is shown that an extension operator \(X'\to Y'\) 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.