Spectrum of weighted composition operators. VI: Essential spectra of \(d\)-endomorphisms of Banach \(C(K)\)-modules (Q2056259)

The paper studies the properties of essential spectra of disjointness preserving operators acting on Banach \(C(K)\)-modules. Under some very mild conditions, the upper semi-Fredholm spectrum of such an operator is rotation invariant. Considered on Kaplansky modules, the spectrum and the essential spectra of operators of the form \(T=wU\) are described completely, where \(w\in C(K)\), \(U\) is a \(d\)-isomorphism, and the spectrum of \(U\) is a subset of the unit circle.