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

2023/07/03 by Arkady Kitover, Kitover, Arkady, Mehmet Orhon +1
Mathematics · #46B60 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Holomorphic and Operator Theory #Primary 47B33 #Secondary 47B48 #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.2307.01112

openalex publication_date 2023/07/03 · openalex created_date 2023/07/05 · openalex updated_date 2026/07/28

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.

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