Uniform dentability, uniform smoothability and approximations to convex sets
The author defines the notions of uniform dentability and uniform smoothability for a Banach space \(X\) and also gives their weak\(^*\) versions. Proving several technically involved lemmas, it is shown that \(X\) is uniformly (resp. \(X^*\) is weak\(^*\) uniformly) dentable if and only if \(X^*\) is weak\(^*\) uniformly smoothable (resp. \(X\) is uniformly smoothable).
scientific article; zbMATH DE number 219353