Norm Attaining Arens Extensions on ℓ1

Abstract EN

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 ℓ1 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.