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

摘要

This paper is concerned with {an extension and reinterpretation} of previousresults on the variational characterization of eigenvalues in gaps of theessential spectrum of self-adjoint operators. {We state} two general abstractresults on the existence of eigenvalues in the gap and a continuationprinciple. Then, these results are applied to Dirac operators in order tocharacterize simultaneously eigenvalues corresponding to electronic andpositronic bound states.