Maximal Accretive Extensions of Schrödinger Operators on Vector Bundles over Infinite Graphs

Given a Hermitian vector bundle over an infinite weighted graph, we define the Laplacian associated to a unitary connection on this bundle and study a perturbation of this Laplacian by an operator-valued potential. We give a sufficient condition for the resulting Schrödinger operator to serve as the generator of a strongly continuous contraction semigroup in the corresponding ℓp-space. Additionally, in the context of ℓ2-space, we study the essential self-adjointness of the corresponding Schrödinger operator