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<p>The well-known Kamowitz–Scheinberg theorem states that if <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$ U $</EquationSource> </InlineEquation> is an automorphism ofa&#xa0;commutative semisimple Banach algebra and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$ U^{n}\neq I $</EquationSource> </InlineEquation> for all <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$ n\in 𝕅 $</EquationSource> </InlineEquation>,then the spectrum of <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$ U $</EquationSource> </InlineEquation> contains the unit circle.In this paper we present some results on the spectrum of weighted automorphismsof unital commutative semisimple Banach algebrasthat considerably strengthen the statement of the Kamowitz–Scheinberg theorem.</p>

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Spectrum of Weighted Composition Operators. Part XII: The Kamowitz–Scheinberg Theorem Revisited

  • 期刊论文

  • 发表日期：

    2026年3月28日

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  • A. Kitover,
  • M. Orhon

摘要

The well-known Kamowitz–Scheinberg theorem states that if $ U $ is an automorphism ofa commutative semisimple Banach algebra and $ U^{n}\neq I $ for all $ n\in 𝕅 $ ,then the spectrum of $ U $ contains the unit circle.In this paper we present some results on the spectrum of weighted automorphismsof unital commutative semisimple Banach algebrasthat considerably strengthen the statement of the Kamowitz–Scheinberg theorem.