Spectrum of Weighted Composition Operators. Part III. Essential spectra of some disjointness preserving operators on Banach lattices

We describe essential (in particular Fredholm and semi-Fredholm) spectra of operators on Banach lattices of the form $T=wU$, where $w$ is a central operator and $U$ is a disjointness preserving operator such that its spectrum $\sigma(U)$ is a subset of the unit circle.