Fixed points of reflections of compact convex sets and a characterization of state spaces of Jordan Banach algebras

TL;DR

This paper establishes a fixed point theorem for reflections on compact convex sets and characterizes state spaces of JB-algebras as those that are strongly spectral and symmetric.

Contribution

It introduces a new fixed point theorem for reflections and provides a novel characterization of JB-algebra state spaces among compact convex sets.

Findings

Fixed point theorem for reflections of compact convex sets

Characterization of JB-algebra state spaces as strongly spectral and symmetric

Provides new insights into the structure of state spaces in Jordan Banach algebras

Abstract

In the present article we prove a fixed point theorem for reflections of compact convex sets and give a new characterization of state space of JB-algebras among compact convex sets. Namely they are exactly those compact convex sets which are strongly spectral and symmetric.