Nonpositive Curvature : a Geometrical Approach to Hilbert-Schmidt Operators ∗

@inproceedings{Larotonda2008NonpositiveC,
title={Nonpositive Curvature : a Geometrical Approach to Hilbert-Schmidt Operators ∗},
author={Gabriel Larotonda},
year={2008}
}

Gabriel Larotonda

Published 2008

We give a Riemannian structure to the set Σ of positive invertible unitized Hilbert-Schmidt operators, by means of the trace inner product. This metric makes of Σ a nonpositively curved, simply connected and metrically complete Hilbert manifold. The manifold Σ is a universal model for symmetric spaces of the noncompact type: any such space can be isometrically embedded into Σ. We give an intrinsic algebraic characterization of convex closed submanifolds M . We study the group of isometries of… CONTINUE READING