摘要
B.B Pande和O.P.Kapoor在[1]中引入了(S)性质。本文引入(WS)性质。它们分别是强光滑性、非常光滑性的推广。利用(S)、(WS)性质,本文分别给出自反空间、强光滑空间、非常光滑空间的特征。证明了X~*有(S)性质且X严格凸则X有(K)性质、(G)性质等几个结论。最后讨论了K—UR、LK—UR空间同(S)性质的关系,在承认连续性的假设下,给出自反空间的一个充分条件。
This paper introduces the WS property and gives respectively the characterization of reflexivity、strongly smooth and very smooth Banach space. Moreover, it discussed the relationship of (S)、(WS) property and (K)、(G) property, contraction basis and (WM) space. Under continuum hypothsis, it gives a sufficient condition of reflexivity Banach space.
