Isometries of infinite dimensional Hilbert geometries

TL;DR

This paper extends the understanding of isometries in Hilbert geometries from finite to infinite dimensions, combining geometric and functional analytic techniques.

Contribution

It generalizes previous finite-dimensional results to infinite-dimensional Hilbert geometries, providing new characterizations of their isometry groups.

Findings

Extended De la Harpe's results to infinite dimensions.

Characterized isometry groups of infinite-dimensional Hilbert geometries.

Used a mix of geometric and functional analytic methods.

Abstract

In this paper we extend results by De la Harpe concerning the isometries of strictly convex Hilbert geometries, and the characterisation of the isometry groups of Hilbert geometries on finite dimensional simplices, to infinite dimensions. The proofs rely on a mix of geometric and functional analytic methods.