A $d$-algebra whose product does not extend to its Dedekind completion

Mohamed Amine Ben Amor

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arXiv · 2610.07425

A $d$-algebra whose product does not extend to its Dedekind completion

Mohamed Amine Ben Amor

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Abstract

We construct a Banach lattice $d$-algebra with a strong order unit whose product has no positive associative bilinear extension to its Dedekind completion. This gives a negative answer to a question of Wickstead and to the $d$-algebra case of a question of Huijsmans. It also disproves an extension theorem of Chil. The example shows that norm completeness and a strong order unit do not ensure that multiplication extends to the Dedekind completion.

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Mohamed Amine Ben Amor. 2026-10-05. A $d$-algebra whose product does not extend to its Dedekind completion. https://arxiv.org/abs/2610.07425

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