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Journal of Lie Theory 33 (2023), No. 1, 361--376
Copyright Heldermann Verlag 2023

Geodesic Bicombings and a Metric Crandall-Liggett Theory

Jimmie D. Lawson
Department of Mathematics, Louisiana State University, Baton Rouge, U.S.A.

We develop an abstract and general Crandall-Liggett theory in the setting of metric geometry that generalizes the well-known one originally developed for solving certain classes of differential equations on Banach spaces. The metric spaces considered are complete metric spaces equipped with a conical geodesic bicombing, a distinguished collection of metric geodesics that satisfy a weak global non-positive curvature condition. The cone of invertible positive linear operators on a Hilbert space, or more generally the cone of positive invertible elements on a unital C*-algebra, equipped with the Thompson metric is a motivating example for the type of metric space we consider. Some examples of application of our results arose in that setting, but generalize to spaces with geodesic bicombings.

Keywords: Geodesic bicombing, conical, Crandall-Liggett, positive cone, C*-algebra.

MSC: 47H20 53C23 49J27 37C10.

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