IAM   02674
INSTITUTO ARGENTINO DE MATEMATICA ALBERTO CALDERON
Unidad Ejecutora - UE
artículos
Título:
Non positively curved metric in the space of positive definite infinite matrices
Autor/es:
ANDRUCHOW, E.; VARELA, A.
Revista:
REVISTA DE LA UNIóN MATEMáTICA ARGENTINA
Editorial:
UMA
Referencias:
Año: 2006
ISSN:
0041-6932
Resumen:
We introduce a Riemannian metric with non positive curvature in the (infinite dimensional) manifold of positive invertible operators of a Hilbert space H, which are scalar perturbations of Hilbert-Schmidt operators. The (minimal) geodesics and the geodesic distance are computed. It is shown that this metric, which is complete, generalizes the well known non positive metric for positive definite complex matrices. Moreover, these spaces of finite matrices are naturally imbedded in this manifold.