ω-非常凸空间与ω-非常光滑空间
ω-VERY CONVEX SPACES AND ω-VERY SMOOTH SPACES

本文研究了ω-非常凸空间和ω-非常光滑空间的问题. 利用局部自反原理和切片证明了ω-非常凸空间和ω-非常光滑空间的对偶关系, 讨论了ω-非常凸空间和ω-非常光滑空间与其它凸性和光滑性的关系, 给出了ω-非常凸空间与ω-非常光滑空间的若干特征刻画, 所得结果完善了关于Banach 空间凸性与光滑性理论的研究.
In this article, we study the problems of about ω-very convex spaces and ω-very smooth spaces. Using the local reflexive principle and the slice of unit sphere, we show that the ω-very convex spaces and ω-very smooth spaces are dual notions and study the relation between ω-very convexity, ω-very smoothness with various convexity and smoothness, and give some characteristic descriptions of ω-very smoothness and ω-very convexity . These results perfect the research on convexity and smoothness about Banach spaces