广义凸性模与一致非方空间  

Generalization modulus of convexity and uniformly non-square space

作　　者：赵亮 韩朝阳 ZHAO Liang;HAN Zhao-yang(School of Science,Harbin University of Science and Technology,Harbin 150080,China)

机构地区：[1]哈尔滨理工大学理学院,哈尔滨150080

出　　处：《哈尔滨商业大学学报（自然科学版）》2020年第4期466-469,共4页Journal of Harbin University of Commerce：Natural Sciences Edition

基　　金：黑龙江省自然科学基金黑龙江省教育厅科学技术研究项目(12541145).

摘　　要：根据广义凸性模的定义与性质,证明了广义凸性模在一致非方Banach空间X中的若干应用.利用广义凸性模的有关性质给出了一致非方的一个新的等价条件:X是一致非方的,当且仅当存在0<δ<1,使得δα(2-2δ)≥2α′,α′=min{α,1-α}由非严格凸的Banach空间单位球面的特点,得到了非严格凸的Banach空间X的单位球面上线段的长度与广义凸性模的一组不等式关系.最后得出了lp(Xi)(1<P<+∞)空间是一致非方的充要条件。According to the definition and properties of generalization modulus of convexity,this paper proved some applications of generalization modulus of convexity in uniform nonsquare Banach spaces.A new equivalent condition for Banach spaces to be uniformly nonsquare was proved.Xwas uniformly non-square if and only if it existed 0<δ<1 makesδα(2-2δ)≥2α′,α′=min{α,1-α}.The characteristics of the unit sphere of Banach that was not strictly convex,a set of inequalities between the length of the line segment on the unit sphere of the non strictly convex Banach spaces and generalization modulus of convexity were obtained.Finally,the necessary and sufficient conditions forlp(Xi)space to be a uniform non square were obtained.

关 键 词：BANACH空间 凸性模 广义凸性模 一致非方 非严格凸空间 lp(Xi)(1 

分 类 号：O177.2[理学—数学]