赋Luxemburg范数的广义Orlicz函数空间中的$\lambda$点和$\lambda$性质

华东师范大学学报(自然科学版) ›› 2012, Vol. 2012 ›› Issue (1): 63-73.

赋Luxemburg范数的广义Orlicz函数空间中的$\lambda$点和$\lambda$性质

石忠锐, 翟佳羽

上海大学数学系, 上海 200444

收稿日期:2011-03-01 修回日期:2011-06-01 出版日期:2012-01-25 发布日期:2012-01-26

$\lambda$ point and $\lambda$ property in generalized Orlicz spaces with Luxemburg norm

SHI Zhong-rui, ZHAI Jia-yu

Department of Mathematics, Shanghai University, Shanghai 200444, China

Received:2011-03-01 Revised:2011-06-01 Online:2012-01-25 Published:2012-01-26

摘要/Abstract

摘要： 为了研究在更一般情形下的Orlicz空间的$\lambda$性质, 借鉴经典Orlicz空间中的方法并发展了广义情形下的新方法, 给出了赋Luxemburg范数的广义Orlicz空间单位球中的点是$\lambda$点的充分必要条件. 这些结果表明, 在某些广义Orlicz空间中, 并不是所有单位球中的点都是$\lambda$点, 这与在经典Orlicz空间中, 单位球中的点都是$\lambda$点的结果是不同的. 最后, 给出了具有$\lambda$性质和一致$\lambda$性质的赋Luxemburg范数广义Orlicz空间的充要条件.

关键词: 广义Orlicz空间, Luxemburg范数, $\lambda$性质, $\lambda$点, 一致$\lambda$性质

Abstract: In this paper, we gave the sufficient and necessary conditions of $\lambda$ point in a generalized Orlicz function space equipped with the Luxemburg norm, by methods used in classical Orlicz spaces and new methods introduced especially for generalized ones. The results indicate the difference between points in the unit balls of classical and that of generalized Orlicz spaces: all of the classical spaces are $\lambda$ points, but some of the generalized spaces are not. Finally, we gave the criteria of the $\lambda$ property and the uniform $\lambda$ property of generalized spaces.

Key words: generalized Orlicz spaces, Luxemburg norm, $\lambda$ property, $\lambda$ points, uniform $\lambda$ property

中图分类号:

O177.2

石忠锐, 翟佳羽. 赋Luxemburg范数的广义Orlicz函数空间中的$\lambda$点和$\lambda$性质[J]. 华东师范大学学报(自然科学版), 2012, 2012(1): 63-73.

SHI Zhong-rui, ZHAI Jia-yu. $\lambda$ point and $\lambda$ property in generalized Orlicz spaces with Luxemburg norm[J]. Journal of East China Normal University(Natural Sc, 2012, 2012(1): 63-73.