A topological characterization of dual strict convexity in Asplund spaces

Abstract Let X be an Asplund space. We show that the existence of an equivalent norm on X having a strictly convex dual norm is equivalent to the dual unit sphere S X ⁎ (equivalently X ⁎ ) possessing a non-linear topological property called (⁎), which was introduced by J. Orihuela, S. Troyanski and the author.