摘要
本文引入了Dunford-Pettis全连续算子的定义,给出了该算子的性质及与其他算子的联系;特别地,给出了它与巴拿赫空间的相对紧Dunford-Pettis性质(DPrcP)的关系.针对Dunford-Pettis全连续性考察了巴拿赫空间具有DPrcP的充分条件.最后在巴拿赫格中研究了Dunford-Pettis全连续算子的控制性.
In this paper, we introduce the definition of Dunford-Pettis completely contin- uous operator. We give some properties of this concept related to some well-known classes of operators, and especially, related to the relatively compact Dunford-Pettis property （DPrcP） of a space X or Y. Then some sufficient conditions for the DPrcP of some Banach spaces, with respect to Dunford-Pettis completely continuity, are verified. Finally, we investigate the dominated property of the Dunford-Pettis completely continuous operators on Banach lattices.
出处
《数学进展》
CSCD
北大核心
2016年第1期122-132,共11页
Advances in Mathematics（China）
基金
supported by NSFC(No.11301285)
