Problèmes de renormages

Abstract

We show that, for every scattered compact space K such that K( (ω 1) = Ø , where ω 1 design the first uncountable ordinal, there exists on b ( K) an equivalent norm such that the dual norm is LUR. Moreover, if K ( ω 0) = Ø, where ω 0 design the first infinite ordinal, the norm on b (K) can be chosen itself LUR. We deduce from this result that, if X and Y are Banach spaces such that X′ and Y′ are WCG, then there exists on X ⊗ ε Y an equivalent LUR norm such that the dual norm is also LUR.