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arXiv · 0808.0955

Unitary orbits in a full matrix algebra

Gabriel Larotonda
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Abstract

The Hilbert manifold $Σ$ consisting of positive invertible (unitized) Hilbert-Schmidt operators has a rich structure and geometry. The geometry of unitary orbits $Ω\subset Σ$ 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 $Σ$ two Riemannian metrics.

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Gabriel Larotonda. 2008-08-07. Unitary orbits in a full matrix algebra. https://arxiv.org/abs/0808.0955

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