Geodesic Bicombings and a Metric Crandall-Liggett Theory
Journal of Lie Theory, Tome 33 (2023) no. 1, pp. 361-376
Voir la notice de l'article provenant de la source Heldermann Verlag
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.
Classification :
47H20 53C23 49J27 37C10
Mots-clés : Geodesic bicombing, conical, Crandall-Liggett, positive cone, C*-algebra
Mots-clés : Geodesic bicombing, conical, Crandall-Liggett, positive cone, C*-algebra
J. D. Lawson. Geodesic Bicombings and a Metric Crandall-Liggett Theory. Journal of Lie Theory, Tome 33 (2023) no. 1, pp. 361-376. http://geodesic.mathdoc.fr/item/JOLT_2023_33_1_a15/
@article{JOLT_2023_33_1_a15,
author = {J. D. Lawson},
title = {Geodesic {Bicombings} and a {Metric} {Crandall-Liggett} {Theory}},
journal = {Journal of Lie Theory},
pages = {361--376},
year = {2023},
volume = {33},
number = {1},
zbl = {07700653},
url = {http://geodesic.mathdoc.fr/item/JOLT_2023_33_1_a15/}
}