Abstract

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 unitarily-invariant and the affiliated permutation-invariant "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 essentially-simple. We show the converse, that essential-simplicity is essential to that process.

Author information

Contact details are reproduced from the original publication and may be historical.

Michael Orlitzky

Dept. of Mathematics and Statistics, University of Maryland Baltimore County, Baltimore, U.S.A.

michael@orlitzky.com

Keywords

  • Normal decomposition system
  • Eaton triple
  • spectral function
  • group majorization
  • Euclidean Jordan algebra

Mathematics Subject Classification

17C20, 17C30, 17C55, 52A41, 90C25

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Suggested citation

M. Orlitzky. “Proscribed Normal Decompositions of Euclidean Jordan Algebras.” Journal of Convex Analysis 29 (2022), No. 3, 755–766. https://doi.org/10.68381/jca29043

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Published by Heldermann Verlag, 2022. Rights now held by Banach Press LLC.