Local uniform convexity and Kadec-Klee type properties in \(K\)-interpolation spaces. I. General theory.
The authors present a systematic study of the interpolation of local uniform convexity and Kadec-Klee type properties in K-interpolation spaces. As a by-product of this study, they show that the theorem of Kadec, namely that each separable Banach space admits an equivalent locally uniformly convex norm, follows directly from their approach (see Corollary 3.6.). Another interesting result is Corollary 5.9: Every locally uniformly convex Banach space with an unconditional basis is isomorphic to a complemented subspace of a locally uniformly convex space with a 1-symmetric basis.
scientific article; zbMATH DE number 2104162