Revisits the Kamowitz–Scheinberg theorem, enhancing spectrum insights in unital commutative semisimple Banach algebras, implying broader applications.
The well-known Kamowitz–Scheinberg theorem states that if U is an automorphism of a commutative semisimple Banach algebra and Uⁿ≠ I for all n∈ , then the spectrum of U contains the unit circle. In this paper we present some results on the spectrum of weighted automorphisms of unital commutative semisimple Banach algebras that considerably strengthen the statement of the Kamowitz–Scheinberg theorem.
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Kitover et al. (2026) studied this question.
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