Perturbation of ℓ1-copies in preduals of JBW⁎-triples

It is known that two normal functionals on a JBW⁎-triple are orthogonal (i.e. they have orthogonal support tripotents) if and only if they are L-orthogonal (meaning that they span an isometric copy of ℓ12). This is shown to be stable under small norm perturbations in the following sense: if the linear span of the two functionals is isometric up to δ>0 to ℓ12, then the functionals are less far (in norm) than ε>0 from two orthogonal functionals, where ε→0 as δ→0. Analogous statements for finitely and even infinitely many functionals hold as well. And so does a corresponding statement for non-normal functionals.