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

Juyoung Jeong () and M. Seetharama Gowda ()
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Juyoung Jeong: Changwon National University
M. Seetharama Gowda: University of Maryland, Baltimore County

Journal of Optimization Theory and Applications, 2024, vol. 202, issue 3, No 11, 1242-1267

Abstract: 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.

Keywords: Fan-Theobald-von Neumann system; Eigenvalue map; Spectral set; Spectral function; Transfer principle; Subdifferential; 17C20; 46N10; 49J52; 52A41; 90C25 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02474-7

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