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    Rights statement: 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, https://doi.org/10.1093/qmath/hay003 is available online at: https://academic.oup.com/qjmath/article/69/3/975/4925263

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The Radical of the Bidual of a Beurling Algebra

Research output: Contribution to journalJournal article

Published
<mark>Journal publication date</mark>1/09/2018
<mark>Journal</mark>The Quarterly Journal of Mathematics
Issue number3
Volume69
Number of pages19
Pages (from-to)975-993
Publication statusPublished
Early online date9/03/18
Original languageEnglish

Abstract

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.

Bibliographic note

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, https://doi.org/10.1093/qmath/hay003 is available online at: https://academic.oup.com/qjmath/article/69/3/975/4925263