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Transfer Principles, Fenchel Conjugate, and Subdifferential Formulas in Fan-Theobald-von Neumann Systems

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Listed:
  • Juyoung Jeong

    (Changwon National University)

  • M. Seetharama Gowda

    (University of Maryland, Baltimore County)

Abstract

A Fan-Theobald-von Neumann system [7] is a triple $$(\mathcal {V},\mathcal {W},\lambda )$$ ( V , W , λ ) , where $$\mathcal {V}$$ V and $$\mathcal {W}$$ W are real inner product spaces and $$\lambda :\mathcal {V}\rightarrow \mathcal {W}$$ 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 decomposition systems (Eaton triples). The present article is a continuation of [9] where the concepts of commutativity, automorphisms, majorization, and reduction were introduced and elaborated. Here, we describe some transfer principles and present Fenchel conjugate and subdifferential formulas.

Suggested Citation

  • Juyoung Jeong & M. Seetharama Gowda, 2024. "Transfer Principles, Fenchel Conjugate, and Subdifferential Formulas in Fan-Theobald-von Neumann Systems," Journal of Optimization Theory and Applications, Springer, vol. 202(3), pages 1242-1267, September.
    • Handle: RePEc:spr:joptap:v:202:y:2024:i:3:d:10.1007_s10957-024-02474-7
    DOI: 10.1007/s10957-024-02474-7
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    References listed on IDEAS

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    1. Defeng Sun & Jie Sun, 2008. "Löwner's Operator and Spectral Functions in Euclidean Jordan Algebras," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 421-445, May.
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