On the stability of self-adjointness of Schrödinger operators under positive perturbations

Abstract

SynopsisWe introduce a class of essentially self-adjoint Schrödinger operators, where essential self-adjointness is stable under positive potential perturbations. We show that this class is “stable” under certain perturbations and contains operators discussed by Simon and Kato. Finally, an extended essentially self-adjointness criterion is given.