Subspaces and Quotients of Banach Symmetric Spaces

TL;DR

This paper establishes a precise criterion for when quotients of Banach symmetric spaces can themselves be endowed with symmetric space structures, exploring the related reflection subspaces and Lie triple systems.

Contribution

It provides a necessary and sufficient condition for symmetric space structures on quotients of Banach symmetric spaces, advancing understanding of their subspace and quotient structures.

Findings

Derived a criterion for symmetric space structures on quotients

Analyzed reflection subspaces and their Lie triple systems

Enhanced understanding of subspace and quotient structures in Banach symmetric spaces

Abstract

We derive a necessary and sufficient condition for the existence of symmetric space structures on quotients of Banach symmetric spaces. Along the way, we investigate the different kinds of reflection subspaces and their Lie triple systems.