赋p-Amemiya范数Musielak-Orlicz序列空间的Kadec-klee性质  

Kadec-klee Property in Musielak-Orlicz of Sequence Space Equipped with p-Amemiya Norm

作　　者：赵丽 崔云安 ZHAO Li;CUI Yun-an(School of Applied Sciences,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：《哈尔滨理工大学学报》2021年第5期157-164,共8页Journal of Harbin University of Science and Technology

基　　金：国家自然科学基金(11871181).

摘　　要：Kadec-klee性质是Banach空间理论一个重要的性质,其与空间的逼近紧及非扩张映射的不动点性质密切相关。基于此给出了赋p-Amemiya范数的Musielak-Orlicz序列空间在单位球面上是H点的充分必要条件,又给出了赋p-Amemiya范数的Musielak-Orlicz序列空间具有Kadec-Klee性质,一致Kadec-klee性,接近一致凸的充分必要条件。As we known,H property is a important property in theory of Banach spaces.It closly connects with the approximation compactness and fixed point property of nonexpansive mapping.In this paper,we give necessary and sufficient conditions for a point in a Musielak-Orlicz sequence spaces equipped with p-Amemiya norm to be an H-point.we give necessary and sufficient conditions for a Musielak-Orlicz sequence spaces equipped with p-Amemiya norm to have the Kadec-Klee property,the uniform Kadec-Klee property and to be nearly uniformly convex.

关 键 词：MUSIELAK-ORLICZ序列空间 p-Amemiya范数 Kadec-klee性质 接近一致凸性 一致Kadec-klee性 

分 类 号：O177.3[理学—数学]