Orlicz空间中单位球面上特殊点的刻画

Characterization of special points of unit sphere in Orlicz spaces

在Orlicz空间中Φ满足Δ2-条件与‖x‖=1蕴含IΦ(x)=1这一条件是等价的,但是,并不知道Orlicz空间单位球面上的何种点满足后一条件.给出了满足上述条件的点的充要判据,并讨论了Orlicz空间的对偶空间中满足f=v+φ(K(v)=,v≠0)这一条件的元素范数可达的充要条件.

In Orlicz spaces,it is well known that Φ satisfies the Δ2-condition if and only if ‖x‖=1 implies IΦ（x）=1.But the question that what kind of points of the unit sphere satisfies the latter condition has not been answered.In this paper,the necessary and sufficient conditions for above special points are given;moreover,criteria in order that f∈S（L°Φ＊） is norm attainable with f=v＋φ（K（v）=,v≠0）are discussed.