Abstract
We obtain norm estimates for the resolvent of the Dirac operator. These estimates verify the key assumptions of an extended version of the Rellich-Kato theorem concerning essential self-adjointness. The application of this abstract theorem then shows that the one-electron Dirac operator can admit a Coulomb potential, for atomic numbers less than or equal to 118, plus a second perturbation which satisfies a mild Stummel type bound, and remain essentially self-adjoint.
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