Norm Attaining Arens Extensions on ℓ 1

Abstract

We study norm attaining properties of the Arens extensions of multilinear forms defined on Banach spaces. Among other related results, we construct a multilinear form on ${\ell }_1$ with the property that only some fixed Arens extensions determined a priori attain their norms. We also study when multilinear forms can be approximated by ones with the property that only some of their Arens extensions attain their norms.