English

A Le Page--Kaplansky theorem characterizing commutative JB*-triples

Functional Analysis 2026-04-15 v1 Operator Algebras

Abstract

We prove that a Le Page-type inequality is also valid for metrically characterizing those JB^*-triples that are commutative. More precisely, we establish that the following statements are equivalent for any JB^*-triple EE: (a)(a) EE is commutative. (b)(b) There exists γ>0\gamma>0 satisfying {a,b,{x,y,z}}γ  ⁣{x,y,{a,b,z}}, for all a,b,x,y,zE.\big\|\{a,b,\{x,y,z\}\}\big\|\leq \gamma \ \! \big\|\{x,y,\{a,b,z\}\}\big\|, \hbox{ for all } a,b,x,y,z\in E.

Cite

@article{arxiv.2604.12924,
  title  = {A Le Page--Kaplansky theorem characterizing commutative JB*-triples},
  author = {Lei Li and Siyu Liu and Antonio M. Peralta},
  journal= {arXiv preprint arXiv:2604.12924},
  year   = {2026}
}
R2 v1 2026-07-01T12:09:10.385Z