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This paper is concerned with an extension and reinterpretation of previous results on the variational characterization of eigenvalues in gaps of the essential spectrum of self-adjoint operators. We state two general abstract results on the existence of eigenvalues in the gap and a continuation principle. Then, these results are applied to Dirac opera- tors in order to characterize simultaneously eigenvalues corresponding to electronic and positronic bound states.

General results on the eigenvalues of operators with gaps, arising from both ends of the gaps. Application to Dirac operators