Banach格上的弱* DP算子

The weak* Dunford-pettis Operators in Banach Lattices

研究巴拿赫格上弱*DP算子的相关性质,基于不交序列思想给出了弱*DP算子的序列刻画。利用构造特殊算子的技巧,得到了使得弱*Dunford-Pettis算子是Dunford-Pettis算子的等价刻画,并且获得了相关的推论。最后给出了使得弱*Dunford-Pettis算子为紧算子的一个充分条件。

Studying properties of weak ＊ Dunford-pettis in Banach lattices, this paper gives a characterization of weak ＊ Dunford-pettis operator based on disjoint sequence. Skills of structuring special operators are used to make weak ＊ Dunford-Pettis operator equivalent to Dunford-Pettis operator and then some relevant inferences are achieved. Finally, a sufficient condition is given to work the weak ＊ Dunford-pettis operator as the compact operator.