Convexity in the interpolation spaces

Abstract

In this work we study if the norms rotund, uniformly rotund, weakly uniformly rotund, locally uniformly rotund or weakly locally uniformly rotund interpolate in the complex or the real interpolation spaces. We will see that the properties uniformly rotund and weakly uniformly rotund interpolate, but the properties locally uniformly rotund or weakly locally unifomly rotund do not interpolate in general except for the dual interpolation couple.