The Order Continuous Norm Operators on Banach Lattices

In term of the equivalent definitions of the order continuous norm operator and the theorem (I),we have arrived at the accordance among the order continuous norm operators,the L-weakly operators and the M-weakly operators on some Banach lattices. At the same time,the dual operators of the order continuous norm operators are also order continuous norm operators.Thereby, we have systematically expounded the essential links among the L-weakly operators, the M-weakly operators, the order continuous norm operators and the dual operators on some Banach Lattices.