Let E and F be Fréchet spaces. We prove that if E is reflexive, then the strong bidual (E ⊗̂εF)″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 ⊗̂εF 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.
CITATION STYLE
Domański, P., & Lindström, M. (1996). Grothendieck spaces and duals of injective tensor products. Bulletin of the London Mathematical Society, 28(6), 617–626. https://doi.org/10.1112/blms/28.6.617
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