Geodesic
Riemannian Metrics on Infinite Dimensional Self-Adjoint Operator Groups
Journal of Lie theory, Tome 26 (2016) no. 3, pp. 717-728
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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.
Classification : 47D03, 58B20, 53C22
Mots-clés : Riemannian-Hilbert manifolds, Banach-Lie general linear group, self-adjoint group 
@article{JLT_2016_26_3_JLT_2016_26_3_a6,
     author = {M. L\'opez Galv\'an},
     title = {Riemannian {Metrics} on {Infinite} {Dimensional} {Self-Adjoint} {Operator} {Groups}},
     journal = {Journal of Lie theory},
     pages = {717--728},
     year = {2016},
     volume = {26},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JLT_2016_26_3_JLT_2016_26_3_a6/}
}
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M. López Galván. Riemannian Metrics on Infinite Dimensional Self-Adjoint Operator Groups. Journal of Lie theory, Tome 26 (2016) no. 3, pp. 717-728. http://geodesic.mathdoc.fr/item/JLT_2016_26_3_JLT_2016_26_3_a6/