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
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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