Une remarque sur les espaces d'interpolation faiblement localement uniformément convexes

Abstract

Let $(A_0,A_1)$ be an interpolation couple, and let $B_j$ be the closure of $A_0^{\ast }\cap A_1^{\ast }$ in $A_j^{\ast }$, $j=0,1$. For every $\theta \in ]0,1[$, there exists a natural one to one contraction $R^{\theta }:A^{\theta }\to (B_0^{\ast },B_1^{\ast }{)}^{\theta }$. For some $\beta \in ]0,1[$, the closure of $R^{\beta }(A^{\beta })$ in $(B_0^{\ast },B_1^{\ast }{)}^{\beta }$ is supposed to be weakly LUR. Then $A^{\theta }=A_{\theta }$ for every $\theta \in ]0,1[$.

12 pages, french. Corrects article with same title appeared in Colloq. Math. Vol. 113, No. 2, 197-204, (2011)

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• Operateurs absolument continus et interpolation