The Grothendieck property for injective tensor products of Banach spaces

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