赋s范数Orlicz函数空间的光滑点

Smooth Points of Orlicz Function Spaces Equipped with S-norm

光滑点是巴拿赫空间几何理论中的重要概念,在估计理论,概率论等领域有重要应用。本文中,首先用凸模引入赋s-范数Orlicz空间对偶空间范数,然后讨论对偶范数的范数可达性,在此基础上给出赋s-范数Or-licz空间的支撑泛函的显式形式,最后给出赋s-范数Orlicz空间光滑点的判据。

Smooth points are important concepts in Banach space geometry theory,which have important applications in estimation theory,probability theory and other fields.In this paper,firstly the dual norm of Orlicz space endowed with s-norm is introduced by convex model and then the norm attainability of dual norm is discussed.On this basis,the explicit form of support functional for Orlicz space endowed with s-norm is given.Finally,a criterion for smooth points in Orlicz space endowed with s-norm is presented.