of perturbations of the elements also in its closed unit ball. This result generalizes [@BecFer Theorem 3.8] where it was proved that finite dimensional C$^*$-algebras have the property $\hbox{\rm{(co)}}$.

preliminaries {#sec: preliminaries}
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Given a Banach space $X$ we will denote by $\mathcal{B}_X$ its closed unit ball.

We recall that a *JB$^*$-triple* is a complex Banach space $\mathcal{U}$ which can be equipped with a continuous triple product $\{\cdot,\cdot,\cdot \}:
\mathcal{U}\times \mathcal{U}\times \mathcal{U} \to \mathcal{U},$ which is symmetric and linear in the first and third variables, conjugate linear in the second variable and satisfies the following axioms

1.  $L(a,b) L(x,y) = L(x,y) L(a,b) + L(L(a,b)x,y)
     - L(x,L(b,a)y),$ where $L(a,b)$ is the operator on $\mathcal{U}$ given by$L(a,b) x = \{a,b,x\};$

2.  $L(a,a)$ is an hermitian operator with non-negative spectrum;

3.  $\|L(a,a)\| = \|a\|^2$.

Examples of JB$^*$-triples include C$^*$-algebras with respect to the triple product defined by $$\label{eq product operators} \{x,y,z\} =\frac12 (x y^* z +z y^*x),$$ and JB$^*$-algebras (in the sense of [@Wri77]) under the triple product $\{x,y,z\}= (x\circ y^*) \circ z + (z\circ y^*)\circ x - (x\circ z)\circ y^*.$ The so-called *ternary rings of operators* (TRO’s) studied, for example, in [@NeaRus] are also examples of JB$^*$-triples.

Suppose $x$ is an element 