Skip to content
DraconiticResearch
Search Sources API
194,161 studies31 sourcesUpdated 8 min ago
PreprintCC BY-NC-ND 4.0arXiv

Tensor Products of Almost f-Algebras: A Counterexample

  • Mohamed Amine Ben Amor
Open at sourcePDFDOICite

Abstract

We show that the natural tensor product multiplication of two Archimedean almost f-algebras does not, in general, extend to their Fremlin tensor product. The two algebras in the counterexample have the same underlying vector lattice C[0,1]. Their multiplications are explicit, positive and nilpotent of index three. The obstruction is the fact that the function (s,t)↦ est does not belong to C[0,1]ftensor C[0,1]. The same construction gives Banach almost f-algebras and has consequences for previously published assertions on Riesz and Fremlin projective tensor products of almost f-algebras.

Related

  1. On a fundamental obstruction in the Derscariu Programme: Failure of Dixmier trace factorisation on infinite tensor products of Toeplitz algebras
    Radu-Daniel Derscariu
    Zenodo (CERN European Organization for Nuclear Research)PreprintCC BY5 citedAlgebra & number theoryOpenAlex
  2. Actions of Fell bundles, II: tensor products and Fourier-Stieltjes algebras
    Erik Bédos, Roberto Conti
    arXivPreprintCC BY-NC-SA 4.0Full textAlgebra & number theoryAnalysis & PDEsarXiv
  3. A counterexample to the periodicity conjecture for finite-dimensional algebras
    Haruhisa Enomoto
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  4. Selfless Reduced Crossed Product C*-Algebras Arising from Almost Periodic Actions
    Syuichi Ohshima
    arXivPreprintCC BY-NC-SA 4.0Full textAnalysis & PDEsarXiv
  5. A Two-Dimensional Counterexample to Radical Equality in Primitive Axial Algebras
    Bo Peng
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{amor2026tensor,
  title = {{Tensor Products of Almost \(f\)-Algebras: A Counterexample}},
  author = {Mohamed Amine Ben Amor},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.33963},
  eprint = {2609.33963},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.33963},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Tensor Products of Almost f-Algebras: A Counterexample
AU  - Mohamed Amine Ben Amor
PY  - 2026
DA  - 2026/09/27
PB  - arXiv
DO  - 10.48550/arxiv.2609.33963
UR  - https://arxiv.org/abs/2609.33963
AB  - We show that the natural tensor product multiplication of two Archimedean almost f-algebras does not, in general, extend to their Fremlin tensor product. The two algebras in the counterexample have the same underlying vector lattice C[0,1]. Their multiplications are explicit, positive and nilpotent of index three. The obstruction is the fact that the function (s,t)↦ e^st does not belong to C[0,1]ftensor C[0,1]. The same construction gives Banach almost f-algebras and has consequences for previously published assertions on Riesz and Fremlin projective tensor products of almost f-algebras.
ER  -