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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 mapsatisfying a Fan-Theobald-von Neumann type inequality together with a conditionfor equality. Examples include Euclidean Jordan algebras, systems induced bycertain hyperbolic polynomials, and normal decomposition systems (Eatontriples). The present article is a continuation of an earlier paper, where theconcepts of commutativity, automorphisms, majorization, and reduction wereintroduced and elaborated. Here, we describe some transfer principles andpresent Fenchel conjugate and subdifferential formulas.

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