p-Uniform Convexity and q-Uniform Smoothness of Absolute Normalized Norms on ℂ2

Abstract

We first prove characterizations of p-uniform convexity and q-uniform smoothness. We next give a formulation on absolute normalized norms on ℂ2. Using these, we present some examples of Banach spaces. One of them is a uniformly convex Banach space which is not p-uniformly convex.