Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The radical of the bidual of a Beurling algebra   We prove that the bidual of a Beurling algebra on $\mathbb{Z}$, considered as
a Banach algebra with the first Arens product, can never be semisimple. We then
show that ${\rm rad\,}(\ell^{\, 1}(\oplus_{i=1}^\infty \mathbb{Z})")$ 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 $\omega$ on
$\mathbb{Z}$ such that the bidual of $\ell^{\, 1}(\mathbb{Z}, \omega)$ contains
a radical element which is not nilpotent.

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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg