Abstract
Let X be a Banach space with the Grothendieck property, Y a reflexive Banach space, and let X ⊗ɛY be the injective tensor product of X and Y. (a) If either X** or Y has the approximation property and each continuous linear operator from X* to Y is compact, then X ⊗ɛY has the Grothendieck property. (b) In addition, if Y has an unconditional finite dimensional decomposition, then X ⊗ɛY has the Grothendieck property if and only if each continuous linear operator from X* to Y is compact.
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