Ideal-Reducibility of Positive Operators on Banach Lattices

This Project  is devoted to the study of the Banach-lattice version of ideal-reducibility of operators. We use similar procedures to introduce the notion of ideal-reducibility of operators on Banach lattices. These results enable us to establish some ideal-triangularizabilty results. For example, we show that each quasinilpotent positive operator on $C({\cal K})$, where ${\cal K}$ is a compact Hausdorff space, is ideal-triangularizable. We also discuss discrete Banach lattices with order continuous norms. We shall also prove that each quasinilpotent positive operator in such Banach lattices is ideal-triangularizable.