Abstract
The Hilbert manifold ∑ ∞ consisting of positive invertible (unitized) Hilbert-Schmidt operators has a rich structure and geometry. The geometry of unitary orbits Ω⊂∑ ∞ is studied from the topological and metric viewpoints: we seek for conditions that ensure the existence of a smooth local structure for the set Ω, and we study the convexity of this set for the geodesic structures that arise when we give ∑ ∞ different Riemannian metrics.
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