A Le Page--Kaplansky theorem characterizing commutative JB*-triples
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866918446349942784 |
|---|---|
| author | Li, Lei Liu, Siyu Peralta, Antonio M. |
| author_facet | Li, Lei Liu, Siyu Peralta, Antonio M. |
| contents | 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 $E$:
$(a)$ $E$ is commutative.
$(b)$ There exists $γ>0$ satisfying $$\big\|\{a,b,\{x,y,z\}\}\big\|\leq γ\ \! \big\|\{x,y,\{a,b,z\}\}\big\|, \hbox{ for all } a,b,x,y,z\in E.$$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_12924 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Le Page--Kaplansky theorem characterizing commutative JB*-triples Li, Lei Liu, Siyu Peralta, Antonio M. Functional Analysis Operator Algebras 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 $E$: $(a)$ $E$ is commutative. $(b)$ There exists $γ>0$ satisfying $$\big\|\{a,b,\{x,y,z\}\}\big\|\leq γ\ \! \big\|\{x,y,\{a,b,z\}\}\big\|, \hbox{ for all } a,b,x,y,z\in E.$$ |
| title | A Le Page--Kaplansky theorem characterizing commutative JB*-triples |
| topic | Functional Analysis Operator Algebras |
| url | https://arxiv.org/abs/2604.12924 |