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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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - The Radical of the Bidual of a Beurling Algebra
AU - White, Jared
N1 - 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
PY - 2018/9/1
Y1 - 2018/9/1
N2 - 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.
AB - 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.
U2 - 10.1093/qmath/hay003
DO - 10.1093/qmath/hay003
M3 - Journal article
VL - 69
SP - 975
EP - 993
JO - The Quarterly Journal of Mathematics
JF - The Quarterly Journal of Mathematics
SN - 0033-5606
IS - 3
ER -