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

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