Some properties which generalize uniform rotundity of Banach spaces (Q1202434)

Several properties (nearly uniform rotundness, \(\Delta\)-uniform rotundness, \(\alpha\)-uniformity) close to uniform rotundity in a Banach space have been introduced by several authors. It is proved that all of them coincide with the class of reflexive Banach spaces with the uniform Kadec-Klee property. The stability of these properties by subspaces, quotients and generalized Banach products is also considered. It is proved also that the uniform Kadec-Klee property is stable for such a product of finite-dimensional Banach spaces.