Riemannian metrics in infinite dimensional self-adjoint operator groups

TL;DR

This paper investigates the geodesic distance in infinite-dimensional self-adjoint operator groups equipped with Riemannian metrics, extending classical results on the completeness of Banach-Lie groups to this broader setting.

Contribution

It introduces a study of geodesic distances in self-adjoint operator groups with Riemannian metrics induced by the infinite trace, extending known completeness results.

Findings

Extended classical Banach-Lie group completeness results

Analyzed geodesic distances in infinite-dimensional operator groups

Provided new insights into Riemannian geometry in operator groups

Abstract

The aim of this paper is the study of the geodesic distance in operator groups with several Riemannian metrics. More precisely we study the geodesic distance in self-adjoint operator groups with the left invariant Riemannian metric induced by the infinite trace and extend known results about the completeness of some classical Banach-Lie groups to this general class.