Abstract
Let X be a Banach lattice and p, p′ be real numbers such that 1 < p, p′<∞ and 1/p + 1/p′ = 1. Then \({\ell_p\hat{\otimes}_FX}\) (respectively, \({\ell_p\tilde{\otimes}_{i}X}\)), the Fremlin projective (respectively, the Wittstock injective) tensor product of ℓ p and X, has reflexivity or the Grothendieck property if and only if X has the same property and each positive linear operator from ℓ p (respectively, from ℓ p′) to X* (respectively, to X**) is compact.
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The first-named author is supported by the NNSF of China, Grant No. 10671048, and the third-named author is partially supported by the NNSF of China, Grant No. 10871213.
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Ji, D., Craddock, M. & Bu, Q. Reflexivity and the Grothendieck property for positive tensor products of Banach lattices-I. Positivity 14, 59–68 (2010). https://doi.org/10.1007/s11117-009-0004-9
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DOI: https://doi.org/10.1007/s11117-009-0004-9