
Journal of Convex Analysis 29 (2022), No. 3, 755766 Copyright Heldermann Verlag 2022 Proscribed Normal Decompositions of Euclidean Jordan Algebras Michael Orlitzky Dept. of Mathematics and Statistics, University of Maryland Baltimore County, Baltimore, U.S.A. michael@orlitzky.com Normal decomposition systems unify many results from convex matrix analysis regarding functions that are invariant with respect to a group of transformations  particularly those matrix functions that are unitarilyinvariant and the affiliated permutationinvariant "spectral functions" that depend only on eigenvalues. Spectral functions extend in a natural way to Euclidean Jordan algebras, and several authors have studied the problem of making a Euclidean Jordan algebra into a normal decomposition system. In particular it is known to be possible with respect to the "eigenvalues of" map when the algebra is essentiallysimple. We show the converse, that essentialsimplicity is essential to that process. Keywords: Normal decomposition system, Eaton triple, spectral function, group majorization, Euclidean Jordan algebra. MSC: 17C20, 17C30, 17C55, 52A41, 90C25. [ Fulltextpdf (115 KB)] for subscribers only. 