Riemannian Metrics on Infinite Dimensional Self-Adjoint Operator Groups

MANUEL LOPEZ GALVAN

JOURNAL OF LIE THEORY

HELDERMANN VERLAG

Lugar: Lemgo; Año: 2016 vol. 26 p. 717 - 728

0949-5932

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. We will focus on Banach-Lie subgroups of the group of all invertible operators which differ from the identity operator by a Hilbert-Schmidt operator.