---
abstract: 'We prove a minimax principle for weakly compact JB$^*$-triples characterizing geometrically the singular values of an element. Among the consequences of this principle we present a Weyl inequality on the perturbation of the singular values and a Cauchy-Poincaré (interlacing) theorem. We also obtain a version of the Ky Fan maximum principle in the setting of weakly compact JB$^*$-triples. We study perturbations of the spectral resolutions showing that small perturbations of an element produces small perturbations of the corresponding spectral resolutions. As a consequence we obtain that weakly compact JB$^*$-triples satisfy the property that perturbations of a convex combination of elements in the closed unit ball coincide with a convex combination of perturbations of the elements also in the closed unit ball. All these results hold true when particularized to weakly compact JB$^*$-algebras.'
address: 'Departamento de An[á]{}lisis Matem[á]{}tico, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain.'
author:
- 'Francisco J. Fernández-Polo'
title: The minimax principle and related topics in the Jordan setting
---

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Introduction {#sec:intro}
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The celebrated minimax principle provides a characterization of the eigenvalues of a symmetric compact operator on a Hilbert space without any reference to eigenvectors or the characteristic polynomial. It is also 