Banach空间的几种光滑性

SOME SMOOTHNESSES OF BANACH SPACES

本文对[1]中的若干结果作了进一步的研究,证明了Banach空间的一致极光滑性与X的F可微性是等价的。文中对Banach空间的一些光滑性(光滑性、很光滑性,强光滑性、一致光滑性、极光滑性、很极光滑性、一致极光滑性)作了统一的研究,找出了它们的本质联系。

In this paper, we furtherly investigate some results in[1], proving that the uniform extreme smoothness of Banach spaces X is equivalent to the F-differentiablity of conjugate space X^(**), some smoothnesses of Banach spaceshave been investigated with the same method,and the relations in nature among them are therefore found out.