The Radical of the Bidual of a Beurling Algebra

White, Jared (2018) The Radical of the Bidual of a Beurling Algebra. The Quarterly Journal of Mathematics, 69 (3). pp. 975-993. ISSN 0033-5606

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We prove that the bidual of a Beurling algebra on Z , considered as a Banach algebra with the first Arens product, can never be semisimple. We then show that rad(ℓ1(⊕∞i=1Z)'') contains nilpotent elements of every index. Each of these results settles a question of Dales and Lau. Finally we show that there exists a weight ω on Z such that the bidual of ℓ1(Z,ω) contains a radical element which is not nilpotent.

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Journal Article
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The Quarterly Journal of Mathematics
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This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Quarterly Journal of Mathematics following peer review. The definitive publisher-authenticated version Jared T White; The radical of the bidual of a Beurling algebra, The Quarterly Journal of Mathematics, Volume 69, Issue 3, 1 September 2018, Pages 975–993, is available online at:
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18 Jan 2018 10:24
Last Modified:
27 Sep 2020 04:18