Banach空间的局部k一致光滑性

Locally k uniformly smoothness of Banach spaces

本文给出三个局部k一致光滑空间的特征,讨论了局部k一致光滑空间和中点局部k一致光滑空间的关系,并证明了局部k一致光滑空间一定是局部(k+1)一致光滑空间,反之不然.

In this paper, three new characterizations of locally k-uniformly smoothness of Banach spaces were obtained and the relation between the locally k-uniformly smoothness and midpoint uniformly locally k-uniformly smoothness were discussed. It was also shown that Xis locally k -uniformly smoothness then Xis locally k ＋ 1-ur：formly smoothness, instead otherwise.