Abstract
Let λ be a reflexive Banach sequence lattice and X be a Banach lattice. In this paper, we show that the positive injective tensor product $$\lambda {\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}}\over \otimes } _{\left| \varepsilon \right|}}X$$ is a Grothendieck space if and only if X is a Grothendieck space and every positive linear operator from λ* to X** is compact.
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