Resumen de Smith's Counterexample about Uniform Rotundity in Every Direction

Manuel Fernández García-Hierro , Isidro Palacios Rubio

• It is an open question when the direct sum of normed spaces inherits uniform rotundity in every direction from the factor spaces. M. Smith [4] showed that, in general, the answer is negative. The purpose of this paper is to carry out a complete study of Smith's counterexample.