Banach空间的ω-非常极凸性、ω-非常极光滑性

ω-very Extreme Convexity and ω-very Extreme Smoothness

引入了Banach空间中ω-非常极凸性与ω-非常极光滑性的概念,讨论了ω-非常极凸空间与ω-非常极光滑空间的对偶性及ω-非常极光滑空间和ω-非常极凸空间与其它空间的关系,给出了ω-非常极凸空间与ω-非常极光滑空间的若干特征刻画,从而完善了Banach空间凸性与光滑性的研究.

In this paper we introduce the concepts of ω-very extreme convexity and ω-very extreme smoothness in Banach space, discuss the dual properties of the ω-very extreme convex space and ω-very extreme smooth space as well as the relationship between the ω- very extreme convex space and ω-very extreme smooth space with the other space.Some characterization of very ω-very extreme convex space and ω- very extreme smooth space is given, which improves the study of the convexity and smoothness of the Banach space.