Journal of Lie Theory

no. 3
Riemannian Metrics on Infinite Dimensional Self-Adjoint Operator Groups
Journal of Lie Theory, Volume 26 (2016) no. 3, pp. 717-728
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.
DOI: 10.5802/jolt.908
Classification: 47D03, 58B20, 53C22
Keywords: Riemannian-Hilbert manifolds, Banach-Lie general linear group, self-adjoint group 
@article{JOLT_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},
     doi = {10.5802/jolt.908},
     zbl = {1354.58009},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.908/}
}
TY  - JOUR
AU  - M. López Galván
TI  - Riemannian Metrics on Infinite Dimensional Self-Adjoint Operator Groups
JO  - Journal of Lie Theory
PY  - 2016
SP  - 717
EP  - 728
VL  - 26
IS  - 3
UR  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.908/
DO  - 10.5802/jolt.908
ID  - JOLT_2016_26_3_a6
ER  - 
%0 Journal Article
%A M. López Galván
%T Riemannian Metrics on Infinite Dimensional Self-Adjoint Operator Groups
%J Journal of Lie Theory
%D 2016
%P 717-728
%V 26
%N 3
%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.908/
%R 10.5802/jolt.908
%F JOLT_2016_26_3_a6
M. López Galván. Riemannian Metrics on Infinite Dimensional Self-Adjoint Operator Groups. Journal of Lie Theory, Volume 26 (2016) no. 3, pp. 717-728. doi: 10.5802/jolt.908

Cited by Sources: