A Le Page--Kaplansky theorem characterizing commutative JB*-triples
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 E: (a) E is commutative. (b) There exists γ>0 satisfying \|\a,b,\x,y,z\\\|≤ γ \ \! \|\x,y,\a,b,z\\\|, for all a,b,x,y,z∈ E.
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