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arXiv · 2209.14175

Commutativity, majorization, and reduction in Fan-Theobald-von Neumann systems

M. Seetharama Gowda·Juyoung Jeong
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Abstract

A Fan-Theobald-von Neumann system is a triple $(V,W,\lambda)$, where $V$ and $W$ are real inner product spaces and $\lambda:V \to W$ is a norm-preserving map satisfying a Fan-Theobald-von Neumann type inequality together with a condition for equality. Examples include Euclidean Jordan algebras, systems induced by certain hyperbolic polynomials, and normal decompositions systems (Eaton triples). In the previous paper (arXiv:1902.06640) we presented some basic properties of such systems and described results on optimization problems dealing with certain combinations of linear/distance and spectral functions. We also introduced the concept of commutativity via the equality in the Fan-Theobald-von Neumann type inequality. In the present paper, we elaborate on the concept of commutativity and introduce/study automorphisms, majorization, and reduction in Fan-Theobald-von Neumann systems.

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M. Seetharama Gowda, Juyoung Jeong. 2022-09-28. Commutativity, majorization, and reduction in Fan-Theobald-von Neumann systems. https://arxiv.org/abs/2209.14175

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