Eigenvalue bounds for non-selfadjoint Dirac operators

In this work we prove that the eigenvalues of $n$-dimensional massive Dirac operator $\mathscr{D}_0 + V$, $n\ge2$, perturbed by a possibly non-Hermitian potential $V$, are localized in union two disjoint disks complex plane, provided $V$ is sufficiently small with respect to mixed norms $L^1_{x_j} L^\infty_{\widehat{x}_j}$, for $j\in\{1,\dots,n\}$. massless case, instead discrete spectrum empty under same smallness assumption on and particular unperturbed operator, namely $\sigma(\mathscr{D}_0+V)=\sigma(\mathscr{D}_0)=\mathbb{R}$. The main tools employ an abstract version Birman-Schwinger principle, which include also study embedded eigenvalues, suitable resolvent estimates Schr\"odinger operator.