A JB*-triple E is commutative if and only if there exists γ > 0 such that the norm of {a,b,{x,y,z}} is at most γ times the norm of {x,y,{a,b,z}} for all elements a,b,x,y,z in E.
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A Le Page--Kaplansky theorem characterizing commutative JB*-triples
A JB*-triple E is commutative if and only if there exists γ > 0 such that the norm of {a,b,{x,y,z}} is at most γ times the norm of {x,y,{a,b,z}} for all elements a,b,x,y,z in E.