• Corpus ID: 247447722

Geometry of infinite dimensional unitary groups: convexity and fixed points

@inproceedings{Miglioli2022GeometryOI,
  title={Geometry of infinite dimensional unitary groups: convexity and fixed points},
  author={Martin Miglioli},
  year={2022}
}
. In this article we study convexity properties of distance functions in infinite dimensional Finsler unitary groups, such as the full unitary group, the unitary Schatten perturbations of the identity and unitary groups of finite von Neumann algebras. The Finsler structures are defined by translation of different norms on the tangent space at the identity. We first prove a convexity result for the metric derived from the operator norm on the full unitary group. We also prove strong convexity results… 

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