Revista de la Unión Matemática Argentina
versión On-line ISSN 1669-9637
ANDRUCHOW, Esteban y VARELA, Alejandro. Non Positively Curved Metric in the Space of Positive Definite Infinite Matrices. Rev. Unión Mat. Argent. [online]. 2007, vol.48, n.1, pp. 7-15. ISSN 1669-9637.
We introduce a Riemannian metric with non positive curvature in the (infinite dimensional) manifold of positive invertible operators of a Hilbert space , 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 .
Palabras clave : positive operator; Hilbert-Schmidt class.