Grothendieck Spaces and Duals of Injective Tensor Products

Abstract

Let E and F be Frechet spaces. We prove that if E is reflexive, then the strong bidual (E⊗eF )′′ b is a topological subspace of Lb(E ′ b, F ′′ b ). We also prove that if moreover E is Montel and F has the Grothendieck property, then E⊗eF has the Grothendieck property whenever either E or F ′′ b has the approximation property. A similar result is obtained for the property of containing no complemented copy of c0.