赋Orlicz范数的Orlicz函数空间的紧强凸性质

Compactly Strongly Convex Property in Orlicz Function Spaces Equipped with the Orlicz Norm

利用Banach空间几何理论中凸性与光滑性的对偶关系,研究了紧强凸性质在赋Orlicz范数的Orlicz函数空间L0M中的刻画问题.首先,给出了赋Luxemburg范数的Orlicz函数空间LM的子空间EM具有S性质的判别准则.然后在赋Orlicz范数Orlicz函数空间L0M中,给出了紧强凸性质的具体刻画,进而得到了这类空间具有强凸性质的充分必要条件.

By the dual relationship of convexity and smoothness in the geometric theory of Banach spaces, the depiction for compactly strongly convex property in Orlicz function spaces LM equipped with the Orlicz norm is in- vestigated. Firstly, the criterion for property S in the subspace EM of Orlicz function spaces LM equipped with the Luxemburg norm is gave. Secondly, the specific characterization for compactly strongly convex property in Orlicz function space LM equipped with the Orlicz norm is presented, and then the necessary and sufficient condition that this kind of space have strongly convex property was obtained.