Isometries of infinite dimensional Hilbert geometries

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.

19 pages, 1 figure. To appear in Journal of Topology and Analysis