Commutativity, Majorization, and Reduction in Fan–Theobald–von Neumann Systems
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Gowda, M. Seetharama, and Juyoung Jeong. “Commutativity, Majorization, and Reduction in Fan–Theobald–von Neumann Systems.” Results in Mathematics 78, no. 3 (2023): 72. https://doi.org/10.1007/s00025-023-01845-2.
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This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s00025-023-01845-2
Abstract
A Fan–Theobald–von Neumann system (Gowda in Optimizing certain combinations of linear/distance functions over spectral sets, 2019. arXiv:1902.06640v2) is a triple (V, W, λ), where V and W are real inner product spaces and λ : V→ 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 Gowda (Optimizing certain combinations of linear/distance functions over spectral sets, 2019. arXiv:1902.06640v2), 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.