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

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