On The Properties Of Special Operators On Banach Lattice

In this paper, we deduce the domination property, lattice order property and duality property of the O-Dunford-Pettis operators on Banach lattices. And we obtain some relationships between the O-Dunford-Pettis operators and other operators.First, we give some sufficient conditions for that an operator dominated by a O-Dunford-Pettis operator is again an O-Dunford-Pettis. And we prove that an operator dominated by other operators such as Dunford-Pettis operator is an O-Dunford-Pettis operator subject to some conditions. In addition we show the existence of the modulus of O-Dunford-Pettis operators. We also present some sufficient conditions under which the modulus an O-Dunford-Pettis operator is again an O-Dunford-Pettis operator. And if the modulu of an operator is O-Dunford-Pettis, we show the operator itself is an O-Dunford-Pettis under some conditions.Then, we give some sufficient conditions for that an O-Dunford-Pettis operator admits a dual operator which is also O-Dunford-Pettis. And we prove that if the dual operator of an operator is O-Dunford-Pettis, the operator itself is also O-Dunford-Pettis under some conditions.At last we obtain some relationships between the O-Dunford-Pettis operators and other operators such as AM-compact operators and Dunford-Pettis operators.