Spectrum of Weighted Composition Operators. Part IX. The spectrum and essential spectra of some weighted composition operators on uniform algebras

Abstract: We obtain some results about the spectrum and the upper semi-Fredholm spectrum of weighted composition operators on uniform algebras, assuming that the corresponding map maps the Shilov boundary onto itself. In particular, it follows from our results that in the case of analytic uniform algebras the spectrum is a connected rotation invariant subset of the complex plane, and that the upper semi-Fredholm spectrum is rotation invariant as well.