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Autore principale: White, Jared T.
Natura: Preprint
Pubblicazione: 2026
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Accesso online:https://arxiv.org/abs/2602.02764
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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.
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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