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® e F)' b is a topological subspace of L b (E' b , F" b ). We also prove that if, moreover, E is Montel and F has the Grothendieck property, then E® e F 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 c n .

Grothendieck operators on tensor products

“…In case of E = C (K) it follows immediately from results of Freniche [Fr2] (compare [DL,Cor. 3.7]) that C (K, F ) [Jh]).…”

Multiresolution analysis for compactly supported interpolating tensor product wavelets

“…Book [41] contains also an introduction to tensor products of Banach spaces. Domański et al [16,17] have done some research on them. Michor [43] has represented tensor products of Banach spaces using category theory.…”

On the Injective Tensor Product of Distinguished Frechet Spaces

“…P is surjective. This is connected with the Radon -Nikodym property and happens, e. g., if E is reflexive (see [6], [7], [ll,Th. 3.21).…”

“…Under certain conditions (e. g. if E or F is reflexive and EL or Fi has the strict approximation property) the strong dual of a distinguished space E&F is canonically isomorphic to Ei&Fg' and the bidual is canonically isomorphic to La(Ei, F") (see [8,Th. 161,[ll], [6,Sec. 31,[lo,Th.…”