Dolbeault J., Esteban M.J., Sere E. On the eigenvalues of operators with gaps. Application to Dirac operators (467K, Postscript) ABSTRACT. This paper is devoted to a general min-max characterization of the eigenvalues in a gap of the essential spectrum of a self-adjoint unbounded operator. We prove an abstract theorem, then we apply it to the case of Dirac operators with a Coulomb-like potential. The result is optimal for the Coulomb potential.