A topological characterization of dual strict convexity in Asplund spaces (Q2304267)

The author gives, for the class of Asplund Banach spaces \(X\), a necessary and sufficient condition that \(X\) admits an equivalent norm whose dual norm is strictly convex, in terms of a purely topological property of the weak\(^*\) topology on \(X^*\) (or its unit sphere), viz., property~\((*)\) introduced in [\textit{J. Orihuela} et al., Proc. Lond. Math. Soc. (3) 104, No. 1, 197--222 (2012; Zbl 1241.46005)].