赋Orlicz范数的Musielak-Orlicz序列空间的暴露点

Exposed points in Musielak-Orlicz sequence spaces endowed with the Orlicz norm

暴露点与强暴露点是Banach空间几何中基本概念,在控制论与逼近论中有广泛的应用,具有鲜明的几何意义.H.Hudzik与崔云安[4]得到弱强暴露与很光滑是一对具有对偶性质的结果,进一步说明暴露性的重要价值.关于Orlicz空间的暴露点和暴露性已全部解决,但在Musielak-Orlicz空间还未见讨论.给出赋Orlicz范数的Musielak-Orlicz序列空间的暴露点的充分必要判别条件,旨在完善与推广暴露性的讨论.

Exposed points and strongly exposed points which are widely used in the theory of approximation and the control theory are basic conceptions in the geometry of Banach space, they have remarkable geometric significance. H. Hudzik and Cui Yunan[4 ] proved the result that weakly strongly exposed points and very smooth points have dual property. This was additional illustrative of the valuable of strongly exposed property. Exposed points and exposed points of Orlicz space have been investigated. The case in Musielak - Orlicz space has never been discussed. The necessary and sufficient conditions of exposed points in Musielak - 0rlicz sequence space with Orlicz norm will be given to improve as well as generalize the discussion of exposed property.