
Journal of Lie Theory 33 (2023), No. 1, 361376 Copyright Heldermann Verlag 2023 Geodesic Bicombings and a Metric CrandallLiggett Theory Jimmie D. Lawson Department of Mathematics, Louisiana State University, Baton Rouge, U.S.A. lawson@math.lsu.edu We develop an abstract and general CrandallLiggett theory in the setting of metric geometry that generalizes the wellknown 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 nonpositive 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, CrandallLiggett, positive cone, C*algebra. MSC: 47H20 53C23 49J27 37C10. [ Fulltextpdf (151 KB)] for subscribers only. 