# 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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