The Radon–Nikodym Property for Tensor Products of Banach Lattices

Abstract

Let 1 p< ∞. We show thatp ˆ ⊗F X, the Fremlin projective tensor product ofp with a Banach lattice X, has the Radon-Nikodym property if and only if X has the Radon-Nikodym property; and thatp ˜ ⊗iX, the Wittstock injective tensor product of � p with a Banach lattice X, has the Radon-Nikodym property if and only if X has the Radon-Nikodym property and each positive operator frompto X is compact, where 1/p + 1/p � = 1 and letp� = c0 if p = 1. Mathematics Subject Classification 2000: 46B22, 46B42, 46M05, 47B65