Extreme points, exposed points, differentiability points in CL-spaces

Cheng, Li-Xin; Li, Min

doi:10.1090/S0002-9939-08-09220-4

Extreme points, exposed points, differentiability points in CL-spaces
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by Li-Xin Cheng and Min Li PDF

Proc. Amer. Math. Soc. 136 (2008), 2445-2451 Request permission

Abstract:

This paper presents a property of geometric and topological nature of Gateaux differentiability points and Fréchet differentiability points of almost CL-spaces. More precisely, if we denote by $M$ a maximal convex set of the unit sphere of a CL-space $X$, and by $C_{M}$ the cone generated by $M$, then all Gateaux differentiability points of $X$ are just $\bigcup$n-s$(C_{M})$, and all Fréchet differentiability points of $X$ are $\bigcup {\mathrm {int}(C_{M})}$ (where n-s$(C_{M})$ denotes the non-support points set of $C_{M}$).

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