Note on Lieb–Thirring type inequalities for a complex perturbation of fractional Laplacian

For $s>0$, let $H_0=(-\Delta)^s$ be the fractional Laplacian. In this paper, we obtain Lieb–Thirring type inequalities for the fractional Schrödinger operator defined as $H=H_0+V$, where $V\in L^p(\mathbb{R}^d), p\ge 1, d\ge 1,$ is a complex-valued potential. Our methods are based on the results of articles by Borichev–Golinskii–Kupin [BGK09] and Hansmann [Han11].