Grothendieck Spaces and Duals of Injective Tensor Products

Let E and F be Fréchet spaces. We prove that if E isreflexive, then the strong bidual is a topological subspace of . We also prove that if, moreover, E is Montel and F has the Grothendieckproperty, then has the Grothendieck property whenever either E or has the approximation property. A similar result is obtainedfor the property of containing no complemented copy of c₀.