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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.
Positivity – Springer Journals
Published: Feb 3, 2009
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