Journal of Lie Theory

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.