  We establish Lieb-Thirring type inequalities for non self-adjoint relatively
compact perturbations of certain operators of mathematical physics. We apply
our results to quantum Hamiltonians of Schr{\"o}dinger and Pauli with constant
magnetic field of strength $b\textgreater{}0$. In particular, we use these
bounds to obtain some information on the distribution of the eigenvalues of the
perturbed operators in the neighborhood of their essential spectrum.
