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On uniformly convex subsets of Banach spaces
Cheng Qingjin *
Department of Mathematics，Xiamen University，XiaMen 361005
*Correspondence author
#Submitted by
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Funding: Specialized Research Fund for the Doctoral Program of Higher Education（No.200803841018）
Opened online: 8 February 2012
Accepted by: none
Citation: Cheng Qingjin.On uniformly convex subsets of Banach spaces[OL]. [ 8 February 2012] http://en.paper.edu.cn/en_releasepaper/content/4462246
 
 
This paper introduces a notion ofuniform convex sets in Banach spaces, which is a localized settingof uniformly convex Banach spaces, and shows that every uniformlyconvex set has many nice properties, such as, every boundeduniformly convex set is weakly compact and admits the Radon-Rieszproperty. It also presents that the metric projection to everynonempty uniformly convex set is always continuous, every convexsubset in a uniformly convex space is uniformly convex and everycompact convex subset in a strictly convex space is also uniformlyconvex.
Keywords:Banach space; uniformly convex space; Radon-Riesz property
 
 
 

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