Decomposition theorems for disjointness preserving operators (Q1316389)

The author proves two different decomposition theorems for disjointness preserving operators on Banach lattices. The first one asserts that a disjointness preserving operator whose spectrum is contained in a sector of angle less than \(\pi\) 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.