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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Authors: Li-Xin Cheng and Min Li
Journal: Proc. Amer. Math. Soc. 136 (2008), 2445-2451
MSC (2000): Primary 46B20, 46G05
Published electronically: February 29, 2008
MathSciNet review: 2390512
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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: http://dx.doi.org/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
Published electronically: February 29, 2008
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.