Location of eigenvalues of non-self-adjoint discrete Dirac operators

Abstract

We provide quantitative estimates on the location of eigenvalues of one-dimensional discrete Dirac operators with complex ${\ell }^p$-potentials for $1\le p\le \infty$. As a corollary, subsets of the essential spectrum free of embedded eigenvalues are determined for small ${\ell }^1$-potential. Further possible improvements and sharpness of the obtained spectral bounds are also discussed.