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arXiv · 2604.08310

Spectral decomposition of doubly power-bounded elements in Banach algebras

Osamu Hatori·Shiho Oi
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Abstract

We establish a characterization of doubly power-bounded elements with finite spectrum in Banach algebras. In particular, we present a spectral decomposition for such elements, extending a classical theorem of Gelfand concerning doubly power-bounded elements with singleton spectrum. Furthermore, we generalize a theorem of Koehler and Rosenthal for doubly power-bounded elements to the setting of Banach algebras. In the final section, we are initiating a study to investigate whether the properties of doubly power-bounded elements can offer insight into the commutativity of Banach algebras.

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Osamu Hatori, Shiho Oi. 2026-04-09. Spectral decomposition of doubly power-bounded elements in Banach algebras. https://arxiv.org/abs/2604.08310

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