Orbits in symmetric spaces

TL;DR

This paper characterizes elements in symmetric spaces on (0,1) or (0,∞) whose orbits form the norm-closed convex hull of their extreme points, extending previous research in the area.

Contribution

It provides a new characterization of elements in symmetric spaces with specific orbit properties, expanding the understanding of geometric structures in these spaces.

Findings

Identifies conditions for orbit convexity in symmetric spaces

Extends previous characterizations by Braverman and Mekler

Enhances understanding of geometric properties of symmetric spaces

Abstract

We characterize those elements in a fully symmetric spaces on the interval $(0,1)$ or on the semi-axis $(0,\infty)$ whose orbits are the norm-closed convex hull of their extreme points. Our results extend and complement earlier work on the same theme by Braverman and Mekler.