Kantorovich Duality and Optimal Transport Problems on Magnetic Graphs

Abstract

We consider Lipschitz- and Arens-Eells-type function spaces constructed for magnetic graphs, which are adapted to this setting from the area of optimal transport on discrete spaces. After establishing the duality between these spaces, we prove a characterization of the extreme points of the unit ball in the magnetic Lipschitz space as well as a result identifying the magnetic Arens-Eells space as a quotient of the classical Arens-Eells space of an associated classical graph called the lift graph.