Radicals of Biduals of Beurling Algebras Can Be Different for the Two Arens Products
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911417724043264 |
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| author | White, Jared T. |
| author_facet | White, Jared T. |
| contents | Let $\operatorname{rad}$ denote the Jacobson radical of a Banach algebra, and let $\Box$ and $\Diamond$ denote the two Arens products on its bidual. We give an example of a Beurling algebra $\mathcal{A}$ for which $\operatorname{rad}(\mathcal{A}^{**}, \Box) \neq \operatorname{rad}(\mathcal{A}^{**}, \Diamond)$, answering a question of Dales and Lau. The underlying group in our example is the free group on three generators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_02764 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Radicals of Biduals of Beurling Algebras Can Be Different for the Two Arens Products White, Jared T. Functional Analysis Group Theory 43A20 (primary), 16N20, 20E05 (secondary) Let $\operatorname{rad}$ denote the Jacobson radical of a Banach algebra, and let $\Box$ and $\Diamond$ denote the two Arens products on its bidual. We give an example of a Beurling algebra $\mathcal{A}$ for which $\operatorname{rad}(\mathcal{A}^{**}, \Box) \neq \operatorname{rad}(\mathcal{A}^{**}, \Diamond)$, answering a question of Dales and Lau. The underlying group in our example is the free group on three generators. |
| title | Radicals of Biduals of Beurling Algebras Can Be Different for the Two Arens Products |
| topic | Functional Analysis Group Theory 43A20 (primary), 16N20, 20E05 (secondary) |
| url | https://arxiv.org/abs/2602.02764 |