An application of the maximum principle to the study of essential self-adjointness of Dirac operators. I

We formulate a theorem saying that the Dirac operator corresponding to a one-electron atomic ion is essentially self-adjoint on the usual domain, provided that the nuclear charge Z is less than 118. Furthermore, for such nuclear charges the domains of the closure of the free particle and total Dirac operators are equal. In the present part I of this paper we prove this theorem for the part of the operator over each of the usual reducing subspaces.