The Order Limited Operators On Banach Lattice

Based on the concepts of AM-compact operator and O-Dunford-Pettis operator,and the structure of Banach lattice, we propose order limited operator defined on Banach lattices. With respect to operator, we mainly investigate the operator’s properties, sequence characterization, lattice order structure, domination property, duality and its factorization and so on.Firstly, we study the sequence characterization of order limited operator, make use of the characterization to obtain judged theorem. And the counterexamples necessity is not established, then, we apply the sequence characterization and decision theorem to solve the factorization, domination property, duality and other issues, and also we get the factorization of the order limited operator by Banach lattices with order continuous norm. Some related results are obtained as well.Then, with the same method through research on AM-compact operator, we receive that the collection of all order limited operator forms a band.Finally, we establish its relationship with other operators, such as compact operator, (L-) weakly compact operator, and (almost) limit operator. It mainly includes two aspects, on the one hand, using operators depict what properties of the domain space or range space has, on the other hand, we give the equivalence conclusions between different operators, when the space meet certain conditions.