On complex perturbations of infinite band Schrödinger operators (Q2822211)

Let \(H_0=-\frac{d^2}{dz^2}+V_0\) be an infinite band Schrödinger operator on \(L^2(\mathbb R)\) with a real valued nonnegative potential \(V_0\in L^\infty (\mathbb R)\). Denote by \(I\) the essential spectrum of \(H_0\). The authors study complex perturbations \(H=H_0+V\) and obtain the Lieb-Thirring type inequalities for the rate of convergence of eigenvalues of \(H\) to the set \(I\). It is assumed that \(V\in L^p(\mathbb R)\) with \(p\geq 2\). If \(\Re V\geq 0\), it is sufficient to assume \(p>1\).