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

  title={Nonpositive Curvature : a Geometrical Approach to Hilbert-Schmidt Operators ∗},
  author={Gabriel Larotonda},
  • 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


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