摘要
对赋Luxember范数或Orlicz范数的Orlicz型序列空间,诸如古典的、广义的及参数式的,本文总结、补充、比较列出了暴露点及暴露性的充分必要刻画,并对以往结果中的错误进行了修正,从而在序列空间方面系统地完成了有关暴露性的刻画。
In this talk, we make a survey for criteria of the exposed points and the exposedness for the sequence spaces of Orlicz type, such as the classical Orlicz spaces, general Orlicz spaces and Musielak-Orlicz spaces, endowed with Luxemburg norm and Orlicz norm respectively. It is well known that explosiveness is basic concept in the geometric theory of Banach spaces. They have numerous application in separation theory and control theory. Criteria for exposed points and strongly exposed points in all classical Orlicz spaces were given in [10-12]. In recent years, Zhao and Cui in [6] discussed the problem in Musielak-Orlicz sequence spaces under some restriction. By counterexamples, we show that the criteria of extreme points in [8] and exposed points in [6] are not true, and we give the criteria for exposed points and strongly exposed points in arbitrary Musielak-Orlicz sequence spaces equipped with Luxemburg norm and Orlicz norm by getting rid of the restriction on Musielak-Orlicz function in [6].
出处
《应用泛函分析学报》
CSCD
2012年第1期14-22,共9页
Acta Analysis Functionalis Applicata
基金
Project Supported in part by the National Natural Science Foundation of China(10971129)
SH(J50101)
