Gorde:
| Egile Nagusiak: | , |
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| Formatua: | Preprint |
| Argitaratua: |
2026
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| Gaiak: | |
| Sarrera elektronikoa: | https://arxiv.org/abs/2604.08310 |
| Etiketak: |
Etiketa erantsi
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| _version_ | 1866917424534650880 |
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| author | Hatori, Osamu Oi, Shiho |
| author_facet | Hatori, Osamu Oi, Shiho |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_08310 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spectral decomposition of doubly power-bounded elements in Banach algebras Hatori, Osamu Oi, Shiho Functional Analysis 47A10, 47B06, 46B04 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. |
| title | Spectral decomposition of doubly power-bounded elements in Banach algebras |
| topic | Functional Analysis 47A10, 47B06, 46B04 |
| url | https://arxiv.org/abs/2604.08310 |