CHARACTERIZATIONS OF GEOMETRICAL PROPERTIES OF BANACH SPACES USING Ψ-Direct SUMS

Abstract

Abstract. Let X be a Banach space and ψ a continuous convex function on ∆ K+1 satisfying certain conditions. Let (X X · · · X) ψ be the ψ-direct sum of X. In this paper, we characterize the K strict convexity, K uniform convexity and uniform non-l N 1 -ness of Banach spaces using ψ-direct sums.