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

Key Points

• The aim is to enhance our understanding of the spectrum of weighted automorphisms in the context of the Kamowitz–Scheinberg theorem.
• Analyzed properties of the spectrum related to weighted automorphisms
• Explored implications within unital commutative semisimple Banach algebras
• Compared results against classical statements of the theorem
• Demonstrated that the spectrum of weighted automorphisms includes key enhancements to the original theorem
• Provided specific conditions under which these enhancements hold
• Presented examples illustrating the new spectrum behaviors