Some geometric properties inherited by the positive tensor products of atomic Banach lattices

Abstract

For Banach lattices X and Y, let X⊗ˆ|π|Y and X⊗̌|ε|Y denote the positive projective and injective tensor products of X and Y, respectively. In this paper, we characterize the inheritance of reflexivity and containment of copies of c0,ℓ1,ℓ∞ by X⊗ˆ|π|Y and X⊗̌|ε|Y from X and Y, when one of them is an atomic Banach lattice. In this case, we also give an affirmative answer to an open question of Jeurnink.