Uniform homeomorphisms between spheres induced by interpolation methods

Abstract

M. Daher [9] showed that if $(X_0,X_1)$ is a regular couple of uniformly convex spaces then the unit spheres of the complex interpolation spaces $X_{\theta }$ and $X_{\eta }$ are uniformly homeomorphic for every $0<\theta ,\eta <1$. We show that this is a rather general phenomenon of interpolation methods described by the discrete framework of interpolation of [15].