Reflexivity and the Grothendieck property for positive tensor products of Banach lattices-II

Published in: Quaestiones Mathematicae
Volume 32, issue 3, 2009, pages: 339–350
DOI: 10.2989/QM.2009.
Author(s): Qingying Bu*Department of Mathematics, USA, Michelle CraddockDepartment of Mathematics, USA, Donghai JiDepartment of Mathematics, P.R. China


Let ϕ be an Orlicz function such that ϕ and its complementary function ϕ* satisfy the Δ2-condition, let ℓϕ be an Orlicz sequence space associated to ϕ, and let X be a Banach lattice. Then ℓϕF X (respectively, ℓϕ ∼⊗i X), the Fremlin projective (respectively, the Wittstock injective) tensor product of ℓϕ and X, has reflexivity or the Grothendieck property if and only if X has the same property and each positive linear operator from ℓϕ (respectively, from ℓϕ*) to X* (respectively, to X**) is compact.

*The author is partially supported by the NSF of China, Grant No. 10871213.

The author is supported by the NSF of China, Grant No. 10671048.

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