Order L-Werkly Compect Operators On Banach Lattices

A huge amount of work has been carried out to study the relationship between M-(L-)weakly compact operator and other operators. In this paper, we study the M-(L-)weak compactness of AM-compact operator, this work is improve the properties of M-and L-weakly compact operator. In the process of studying the relationship between M-(L-)weakly compact operator and AM-compact operator, we introduce a new class operator which is called order L-weakly compact operator. The operator puts the order interval into L-weakly compact set. Then we investigate its controllability, conjugacy, order weak compactness and (O) Dunford-Pettis properties.The main results:1、We study the relationship between AM-compact operator and M-(L-)weakly compact operator. It maily include AM-compact operator is M-(L-) weakly compact operator. Conversely, we also get some results that M-(L-) weakly compact operator is AM-compact operator.2、This paper mainly research some basic properties of order L-weakly compact operator. Firstly, we give the concept of order L-weakly compact operator, then study its product operator and the space conditions of order L-weakly compact operator’s existence.Secondly we discuss controllability of order L-weakly compact operator. Finally, we study the conjugate of order L-weakly compact operator and we obtain some good conclusions.3、At last,we research the order weak compactness, L-weak compactness,(O) Dunford-Pettis property and AM-compactness of order L-weakly compact operators.