Bidual extensions of Riesz multimorphisms

Abstract

We prove that all Arens extensions of finite rank Riesz multimorphisms taking values in Archimedean Riesz spaces coincide and are Riesz multimorphisms. We also prove that, for a class of Banach lattices F, which includes F=c0,ℓp,c0(ℓp),ℓp(c0), ℓp(ℓs),1<p,s<∞, among many others, all Aron-Berner extensions of any F-valued Riesz multimorphism between Banach lattices are Riesz multimorphisms.