Banach格上的无界绝对弱收敛的弱~*Dunford-Pettis算子

Uaw-w~* Dunford-Pettis Operators on Banach lattices

为进一步研究Banach格上算子的性质,首先,给出无界绝对弱收敛的弱~*Dunford-Pettis算子的定义.其次,通过构造不交序列,探究无界绝对弱收敛的弱~*Dunford-Pettis算子的等价刻画和控制性,并获得了相关推论.最后,研究了该算子与弱~*Dunford-Pettis算子、极限算子和紧算子间的关系.

For the further study of the property of operators on Banach lattices, firstly, we give the definition of uaw-w^*Dunford-Pettis operator. Secondly, by constructing the disjoint sequence, we explore the equivalent characterization and domination property of uaw-w^*Dunford-Pettis operator, and relevant inferences are achieved. Finally, we study the relationships between uaw-w^*Dunford-Pettis operator and weak^*Dunford-Pettis operator, limit operator and compact operator.