Geodesic
Riemannian Metrics on Infinite Dimensional Self-Adjoint Operator Groups
Manuel López Galván1
1Instituto Argentino de Matemática "Alberto P. Calderón", Saavedra 15 (C.P. 1083), Buenos Aires, Argentina
Journal of Lie Theory, Tome 26 (2016) no. 3, pp. 717-728

Voir la notice de l'article provenant de la source Heldermann Verlag

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

Manuel López Galván  1

1 Instituto Argentino de Matemática "Alberto P. Calderón", Saavedra 15 (C.P. 1083), Buenos Aires, Argentina 
Manuel 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/JOLT_2016_26_3_a6/
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     author = {Manuel 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/JOLT_2016_26_3_a6/}
}
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