Spectral enclosures for non-self-adjoint discrete Schr\"odinger operators

We study location of eigenvalues of one-dimensional discrete Schr"odinger operators with complex ${\mathrm{\ell }}^p$-potentials for $1\le p\le \mathrm{\infty }$. In the case of ${\mathrm{\ell }}^1$-potentials, the derived bound is shown to be optimal. For $p>1$, two different spectral bounds are obtained. The method relies on the Birman-Schwinger principle and various techniques for estimations of the norm of the Birman-Schwinger operator.