On the Asplund property of locally convex spaces (Q1353651)

The authors study Fréchet differentiability of continuous convex functions on locally convex spaces and characterize the Asplund property in geometric terms, such as slices, strongly exposed points, and dentable sets in locally convex spaces. Among other things, the authors prove the Mazur theorem for a separable Banach space, which was a starting point for the theory of differentiability of convex functions, still holds in separable Baire locally convex spaces by a different method from \textit{Wu Congxin} and \textit{Cheng Lixin} [``Differentiability of convex functions on locally convex spaces. I'', J. Harbin Inst. Tech. E-1, No. 1, 7-12 (1994)] and prove that if the dual space of a Baire locally convex space is separable, then the Baire locally convex space has the Asplund property.