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

Author(s): Li-Xin Cheng; Min Li
Journal: Proc. Amer. Math. Soc. 136 (2008), 2445-2451.
MSC (2000): Primary 46B20, 46G05
Posted: 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}$).

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Additional 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

DOI: 10.1090/S0002-9939-08-09220-4
PII: S 0002-9939(08)09220-4
Keywords: Extreme point, exposed point, differentiability point, CL-space and Banach space
Received by editor(s): December 18, 2006
Posted: February 29, 2008
Communicated by: N. Tomczak-Jaegermann
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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