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

Abstract

A Fan-Theobald-von Neumann system [7] is a triple \((\mathcal {V},\mathcal {W},\lambda )\), where \(\mathcal {V}\) and \(\mathcal {W}\) are real inner product spaces and \(\lambda :\mathcal {V}\rightarrow \mathcal {W}\) 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.