局部一致光滑空间与局部完全k光滑空间

On the Locally Uniformly Smooth and Locally Fully k-Smooth Spaces

讨论了局部一致光滑、局部完全k光滑、局部k一致光滑、一致极光滑与(WM)*性质的关系.利用Banach空间理论的方法,得到了自反局部一致光滑空间的一个充分必要条件.在自反空间假设下,得到了局部一致光滑空间的另一个充分必要条件.

In this paper, the relationship among the locally uniformly smoothness, locally fully k-smoothness,locally k-uniformly smoothness,uniformly extremely smoothness and property （WM）^＊~ are further studied. By the method of Banach space theory, a necessary and sufficient condition of reflexive locally uniformly smooth space is obtained. Also, under the condition of reflexive space, another necessary and sufficient of locally uniformly smooth space is obtained.