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Bibliographic Details
Main Authors: Hatori, Osamu, Oi, Shiho
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2604.08310
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Table of Contents:
  • 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.