Aron–Berner extensions of almost Dunford–Pettis multilinear operators.

We study when Aron–Berner extensions of (separately) almost Dunford–Pettis multilinear operators between Banach lattices are (separately) almost Dunford–Pettis. For instance, for a σ -Dedekind complete Banach lattice F containing a copy of ℓ ∞ , we characterize the Banach lattices E 1 , ... , E m for which every continuous m-linear operator from E 1 × ⋯ × E m to F admits an almost Dunford–Pettis Aron–Berner extension. Illustrative examples are provided. [ABSTRACT FROM AUTHOR]