Let X be a Banach lattice and p, p be real numbers such that 1< p, p <∞ and 1/ p + 1/ p = 1. Then p⊗F X (respectively, p⊗i X ), the Fremlin projective (respectively, the Wittstock injective) tensor product of p and X , has reflexivity or the Grothendieck property if and only if X has the same property and each positive linear operator from p (respectively, from p ) to X * (respectively, to X * * ) is compact.
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