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.

中文翻译：

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Asplund空间中对偶严格凸性的拓扑表征

令 $X$ 为 Asplund 空间。我们证明了在具有严格凸对偶范数的 $X$ 上的等效范数的存在等价于具有非线性拓扑性质的双单位球面 $S_{X^*}$（等价于 $X^*$） ($*$)，由 J. Orihuela、S. Troyanski 和作者介绍。