Jean-Claude Cuenin: Eigenvalue estimates for non-selfadjoint Dirac operators on the real line

We show that the non-embedded eigenvalues of the Dirac operator on the real line with a generally non-hermitian potential lie in the disjoint union of two disks in the right and left half planes, respectively, provided that the L1-norm of Tr(sqrt(V*V)) is bounded from above by the rest energy of the particle. This is to be contrasted with a result of Abramov, Aslanyan and Davies which bounds the absolute values of non-positive eigenvalues of Schrödinger operators with complex potentials in one dimension in terms of the L1-norm of V.