IAM   02674
INSTITUTO ARGENTINO DE MATEMATICA ALBERTO CALDERON
Unidad Ejecutora - UE
artículos
Título:
Non positive metric in the space of positive definite infinite matrices
Autor/es:
E. ANDRUCHOW, A. VARELA
Revista:
REVISTA DE LA UNIóN MATEMáTICA ARGENTINA
Editorial:
Unión Matemática Argentina
Referencias:
Lugar: Bahía Blanca; Año: 2007 vol. 48 p. 7 - 7
ISSN:
0041-6932
Resumen:
We introduce a Riemannian metric with non positive curvature in the (in nite dimensional) manifold 1 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 de nite complex matrices. Moreover, these spaces of nite matrices are naturally imbedded in 1.1 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 de nite complex matrices. Moreover, these spaces of nite matrices are naturally imbedded in 1.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 de nite complex matrices. Moreover, these spaces of nite matrices are naturally imbedded in 1.1.