中文摘要：

在一些光滑和 weak~ 之间的关系 * 双 Banach 空间 X~ 的标准 asymptotic 性质 * 被学习。主要结果是下列。假定 X 是弱顺序的完全的 Banach 空间，那么， X 是 Frechet 可辨如果并且仅当X~*有 B (X)-ANP-Ⅰ， X 是 quasi-Frechet 可辨如果并且仅当X~*有 B (X)-如果并且仅当， ANP -Ⅱ和 X 是很光滑的X~*有 B (X)- ANP -Ⅱ'。一个新本地标准 asymptotic 性质也被介绍，并且在这种之中的关系和一些拓扑的性质被讨论。另外，这篇论文把一个否定答案给胡和林在公牛提出的待研究的问题。南。数学。Soc， 45， 1992。

英文摘要：

The relationship between some smoothness and weak asymptotic-norming properties of dual Banach space X is studied. The main results are the following. Suppose that X is weakly sequential complete Banach space, then X is Frechet differentiable if and only if X has B （X）- ANP -I, X is quasi-Frechet differentiable if and only if X has B（X）- ANP -H and X is very smooth if and only if X has B（X）- ANP -Ⅱ. A new local asymptotic-norming property is also introduced, and the relationship among this one and other local asymptotic-norming properties and some topological properties is discussed. In addition, this paper gives a negative answer to the open question raised by Hu and Lin in Bull. Austral. Math. Soc,45,1992.