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

TL;DR

This paper explores transfer principles and conjugate/subdifferential formulas within Fan-Theobald-von Neumann systems, extending previous work on their structure, automorphisms, and majorization properties in inner product spaces.

Contribution

It introduces transfer principles and derives Fenchel conjugate and subdifferential formulas for Fan-Theobald-von Neumann systems, expanding the theoretical framework of these mathematical structures.

Findings

Established transfer principles for Fan-Theobald-von Neumann systems

Derived Fenchel conjugate formulas for functions on these systems

Provided subdifferential characterizations within the framework

Abstract

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.