Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9500478 | Differential Geometry and its Applications | 2005 | 22 Pages |
Abstract
A riemannian metric is introduced in the infinite dimensional manifold Σn of positive operators with rank n<â on a Hilbert space H. The geometry of this manifold is studied and related to the geometry of the submanifolds Σp of positive operators with range equal to the range of a projection p (rank of p=n), and Pp of selfadjoint projections in the connected component of p. It is shown that these spaces are complete in the geodesic distance.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Esteban Andruchow, Alejandro Varela,