Extreme points, exposed points, differentiability points in CL-spaces
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- by Li-Xin Cheng and Min Li
- Proc. Amer. Math. Soc. 136 (2008), 2445-2451
- DOI: https://doi.org/10.1090/S0002-9939-08-09220-4
- Published electronically: February 29, 2008
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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 $C_{M}$).References
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Bibliographic Information
- Li-Xin Cheng
- Affiliation: Department of Mathematics, Xiamen University, Xiamen 361005, People’s Republic of China
- Email: lxcheng@xmu.edu.cn
- Min Li
- Affiliation: Department of Mathematics, Xiamen University, Xiamen 361005, People’s Republic of China
- Email: jslimin@163.com
- Received by editor(s): December 18, 2006
- Published electronically: February 29, 2008
- Communicated by: N. Tomczak-Jaegermann
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 2445-2451
- MSC (2000): Primary 46B20, 46G05
- DOI: https://doi.org/10.1090/S0002-9939-08-09220-4
- MathSciNet review: 2390512