商空间的k-严格凸继承性  

On the Heredity of k-Rotundity of Quotient Spaces

作　　者：王宏志[1] 段丽芬[1] 崔云安[2] 

机构地区：[1]通化师范学院数学系,吉林通化134002 [2]哈尔滨理工大学应用科学学院,黑龙江哈尔滨150080

出　　处：《江西师范大学学报（自然科学版）》2010年第3期280-282,共3页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金(10571037)资助项目

摘　　要：利用Banach空间几何理论讨论了商空间对它的原空间k-严格凸继承性问题,得到了Banach空间X以它的可逼近子空间M为模的商空间X/M对X的k-严格凸性具有继承性,推广了前人的结果.同时,以一般Orlicz空间为例,说明了上述结论成立和可逼近条件是必要的.By a geometry of Banach spaces method the characterizations over a Heredity of k-rotundity problem about a quotient space to its original space is discussed.It is presented that if X is a Banach space with k-rotundity and M is proximal in X,then the quotient space X/M has also k-rotundity.Moreove,taking the example of Orlicz space generalized any Orlicz function,it points out that the condition making the above conclusion tenable is essential in general.

关 键 词：商空间 K-严格凸 继承性 可逼近 

分 类 号：O177.3[理学—数学]