Year: 2026
Type: preprint
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 \((s,t)\mapsto e^{st}\) 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.
Source: arXiv (Cornell University)
Author: Amor, Mohamed Amine Ben
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214732808