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PreprintCC BY-NC-ND 4.0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{amor2026dalgebra,
  title = {{A $d$-algebra whose product does not extend to its Dedekind completion}},
  author = {Mohamed Amine Ben Amor},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.07425},
  eprint = {2610.07425},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.07425},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - A d-algebra whose product does not extend to its Dedekind completion
AU  - Mohamed Amine Ben Amor
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2610.07425
UR  - https://arxiv.org/abs/2610.07425
AB  - 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.
ER  -