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Abstract: The Hilbert manifold $\Sigma$ consisting of positive invertible unitizedHilbert-Schmidt operators has a rich structure and geometry. The geometry ofunitary orbits $\Omega\subset \Sigma$ is studied from the topological andmetric viewpoints: we seek for conditions that ensure the existence of a smoothlocal structure for the set $\Omega$, and we study the convexity of this setfor the geodesic structures that arise when we give $\Sigma$ two Riemannianmetrics.



Author: Gabriel Larotonda

Source: https://arxiv.org/







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