  Two normal functionals on a JBW$^*$-triple are known to be orthogonal if and
only if they are $L$-orthogonal (meaning that they span an isometric copy of
$\ell_1(2)$). 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
$\delta>0$ to $\ell_1(2)$, then the functionals are less far (in norm) than
$\eps>0$ from two orthogonal functionals, where $\eps\to0$ as $\delta\to0$.
Analogous statements for finitely and even infinitely many functionals hold as
well. And so does a corresponding statement for non-normal functionals. Our
results have been known for C$^*$-algebras.
