Radicals of Biduals of Beurling Algebras Can Be Different for the Two Arens Products
Abstract
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.
Fields of Study & Subjects
Advanced Operator Algebra Research
Advanced Banach Space Theory
Advanced Topics in Algebra
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 2 February 2026
- Document type
- Preprint