compact operator on a Hilbert space.

The minimax principle can be stated for a non-necessarily symmetric compact operator, $A$, replacing the eigenvalues of $A$ with its singular values (the eigenvalues of $(AA^*)^{\frac 12}$) and the inner products $<A\varphi, \varphi>$ with $\|A\varphi\|$.

Although Weyl’s inequality shows that there is a dependence between the distance of the corresponding eigenvalues of two compact operators this is no longer true when dealing with the corresponding eigenvectors. However, C. Davis proved that there is such a relation between the corresponding spectral resolutions of the operators whenever they are “close enough” (see [@Dav]). As observed by J. Becerra and the author of this note in [@BecFer Theorem 3.6], it can derived from Davis’ results the continuity of the spectral resolutions in case of non-necessary symmetric elements in finite dimensional C$^*$-algebras.

The main goal of this work is to extend all these results to the Jordan setting, where by Jordan setting we mean the category of JB$^*$-algebras (the complexifications of JB-algebras) and their ternary generalization JB$^*$-triples. We recommend [@HanStor] as a reference book on JB-algebras while in section \[sec: preliminaries\] we will survey some basics on JB$^*$-triples.

In this non-associative setting we only have been able to 