Maximal accretive extensions of Schr\"odinger operators on vector bundles over infinite graphs

Abstract

Given a Hermitian vector bundle over an infinite weighted graph, we define the Laplacian associated to a unitary connection on this bundle and study the essential self-adjointness of a perturbation of this Laplacian by an operator-valued potential. Additionally, we give a sufficient condition for the resulting Schr\"odinger operator to serve as the generator of a strongly continuous contraction semigroup in the corresponding l^{p}-space.