The minimax principle and related topics in the Jordan setting
Francisco J. Fern\'andez-Polo

TL;DR
This paper establishes a minimax principle for weakly compact JB*-triples, leading to new inequalities and theorems about singular values, spectral resolutions, and perturbations, extending classical results to this algebraic setting.
Contribution
It introduces a minimax principle for JB*-triples and derives related spectral and perturbation results, generalizing known theorems to this non-associative algebraic framework.
Findings
A minimax principle characterizes singular values in JB*-triples.
Weyl inequality and Cauchy-Poincaré interlacing theorem are established.
Perturbation stability of spectral resolutions and convex combinations is demonstrated.
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-Poincar\'e (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…
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