Decomposition Theorems for Disjointness Preserving Operators

Two different decomposition theorems for disjointness preserving operators on Banach lattices are proved. The first one asserts that a disjointness preserving operator whose spectrum is contained in a sector of angle less than π can be decomposed into a sum of a central operator and a quasi-nilpotent operator. The second one asserts that if T is a disjointness preserving operator on an order complete Banach lattice such that its adjoint T′ is also a disjointness preserving operator, then T can be decomposed into a direct sum of its strictly periodic and aperiodic parts. The latter generalizes an earlier result. Various consequences of these results are given.