Problèmes de renormages

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.