Banach格上的几乎L-Dunford-Pettis性质

Almost L-Dunford-Pettis Property in Banach Lattices

引入几乎L-Dunford-Pettis集,根据几乎L-Dunford-Pettis集定义的启发给出Banach格上的几乎L-Dunford-Pettis性质的定义,研究几乎L-Dunford-Pettis性质与Banach格的某些性质以及算子(不交Dunford-Pettis全连续算子,弱紧算子)之间的关系,并考虑几乎L-Dunford-Pettis性质与弱Dunford-Pettis性质之间的联系.

In this paper,we introduce the concept of almost L-Dunford-Pettis sets in Banach lattices,and then give the definition of almost L-Dunford-Pettis property in Banach lattices.A characterization of the almost L-Dunford-Pettis property with respect to some properties of Banach lattices and operators(disjoint DunfordPettis completely continuous,weak compact operators)is given.Finally,we study the relationship between almost L-Dunford-Pettis property and weak DunfordPettis property.