应用泛函分析学报2001，Vol.3Issue(2)：120-128,9.
Banach空间的p-Asplund伴随空间
On the p-Asplund Space of a Banach Space
摘要
Abstract
Recently, a sequence of articles studied the Frechet differentiability property of convex functions on general Banach spaces and even on topological linear spaces. Cheng et al introduced the notion of the FDP (Frechet differentiability property) of convex functions: an extended real valued proper convex function f on a Banach space E is said to have the FDP if every continuous convex function g with g≤f on E is Frechet differentiable on a dense Gδ subset of E. This paper mainly shows that all such continuous convex functions f on the space E are exactly all continuous convex functions on a locally convex space (E, τ) for some suitably locally convex topology τ, that the space (E, τ) is normable if and only if E is an Asplund space. It also presents a revised version of the main theorems of Cheng et al.关键词
Frechet可微性/Banach空间/局部凸空间Key words
convex function/differentiability/Asplund space/Banach space分类
数理科学引用本文复制引用
程立新..Banach空间的p-Asplund伴随空间[J].应用泛函分析学报,2001,3(2):120-128,9.基金项目
Supported partially by the NSF of China (No. 100711063) and by the NSF of Fujian Province (No.F00021) （No. 100711063）
