Transfer principles, Fenchel conjugate and subdifferential formulas in Fan-Theobald-von Neumann systems

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 decomposition systems (Eaton triples). The present article is a continuation of an earlier paper, 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.