复凸性与复光滑性

COMPLEX CONVEXITY AND COMPLEX SMOOTHNESS

在本文中,我们证明了复 Banach 空间 X 的每个两维商空间复严格凸是 X 复严格凸的充分条件和 X~*是复严格凸的当且仅当 X 的每个两维商空间是复光滑的。我们还证明了 V.Istrǎtescu在[7]中定义的复一致光滑与一致光滑是等价的。

In this paper,we show that every two—dimensional quotient subspace ofcomplex Banach space X is complex strictly convex is a sufficient condition for Xto be a complex strictly convex space,and X is complex strictly convex if and ifevery two-dimensional quotient subspace of X is complex smooth.We also showthat complex uniform smooth(which was defined by V.Istrǎtescu in [7])isequivalent to uniform smooth.