Banach空间中的一致可凸化集  

Uniformly convexifiable subsets of Banach spaces

作　　者：李克华[1] 罗春燕 王翠玲 LI Kehua;LUO Chunyan;WANG Cuiling(School of Mathematics&Statistics,Xiamen University of Technology,Xiamen,Fujian 361024,China;School of Mathematical Sciences,Xiamen University,Xiamen,Fujian 361005,China)

机构地区：[1]厦门理工学院数学与统计学院,福建厦门361024 [2]厦门大学数学科学学院,福建厦门361005

出　　处：《内江师范学院学报》2025年第4期43-46,80,共5页Journal of Neijiang Normal University

基　　金：国家自然科学基金项目(12071389)。

摘　　要：文章证明了在Lebesgue函数空间L_(1)[0,1]上,可明确构造一个局部一致凸和各向一致凸的等价范数,使得在此范数下,L_(1)[0,1]中的每个弱紧凸集均为一致凸集.It is proved that on the Lebesgue functional space L_1[0,1],one can explicitly construct an equivalent norm which is locally uniformly convex and uniformly convex in every direction,such that every weakly compact convex set in L_1[0,1] is uniformly convex under this norm.

关 键 词：BANACH空间 一致凸空间 一致可凸化集 

分 类 号：O177[理学—数学]