Further Research On Properties Of Order Dunford-pettis Operators

Order D-P operator is a new operator which was introduced in2012in studying D-P operator. Some basic properties of Order D-P operator have been researched, such as the space assembled by Order D-P operator, left and right ideals and the relationship with other operators (such as Almost D-P operator, D-P operator). Howerver, the dual and control property of Order D-P operator have not been studied detailly. And the relationship between other operators and Order D-P operator is not specifically discussed. Based on relevant conclusions, we further study Order D-P operator related properties.Here are the main contents of this paper.1、We introduce operators along with the research of D-P operator and D-P set. First, we collect and analyze properties of D-P operator, almost D-P operator, weak D-P operator and other related operators. We give current relevant conclusions of Order D-P operator to further research.2、We mainly study the dual property of Order D-P operator. The necessary conditions are goted when it satisfies the dual property. A operator is Order D-P when its dual operator is Order D-P, and necessary properties of space are obtained.3、We discuss necessary and sufficient conditions of their space when the Order D-P operator controlled by positive operator is also Order D-P operator.4、We study the Order D-P of Order weakly compact operator. It discusses the properties of the space while each order weak compact operator is order D-P operator,then get necessary conditions of their space.5、The relationship between Order D-P operator and Semi-compact operator between is studied from two sides. We study necessary properties of space when any positive Order D-P operator is Semi-compact operator. On the other hand necessary conditions for space is also discussed if any Semi-compact operator is Order D-P operator.