On the Eigenvalues of Operators with Gaps. Application to Dirac Operators

Abstract

This paper is devoted to a general min-max characterization of the\neigenvalues in a gap of the essential spectrum of a self-adjoint unbounded\noperator. We prove an abstract theorem, then we apply it to the case of Dirac\noperators with a Coulomb-like potential. The result is optimal for the Coulomb\npotential.\n An erratum is appended at the end of the tex.\n