K一致光滑空间的特征

Equivalence of Some Different Definitions of K-uniformly Smooth Space

讨论了几种不同形式的K一致光滑空间的定义,并指出这几种形式的K一致光滑空间定义实质上是等价的.作为K一致光滑空间的应用,得到了K一致光滑空间的两个重要性质,并证明了这两个重要性质都是一个Banach空间成为K一致光滑空间的充分条件.

Some different definitions of K-uniformly smooth space are discussed, and these definitions are equivalent in essence. As the application of K-uniformly smooth space, two important properties are obtained, and it is proved that the properties are sufficient conditions for a Banach space to be K-uniformly smooth space.