Journal of Lie Theory 26 (2016), No. 3, 717--728
Copyright Heldermann Verlag 2016
Riemannian Metrics on Infinite Dimensional Self-Adjoint Operator Groups
Manuel López Galván
Instituto Argentino de Matemática "Alberto P. Calderón", Saavedra 15 (C.P. 1083), Buenos Aires, Argentina
mlopezgalvan@hotmail.com
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.
Keywords: Riemannian-Hilbert manifolds, Banach-Lie general linear group, self-adjoint group.
MSC: 47D03; 58B20, 53C22
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