On non-selfadjoint perturbations of infinite band Schrödinger operators and Kato method

Abstract

Let $ H_0=-\dd+V_0 $ be a multidimensional Schrödinger ope\-rator with a real-valued potential and infinite band spectrum, and $H=H_0+V$ be its non-selfadjoint perturbation defined with the help of Kato approach. We prove Lieb--Thirring type inequalities for the discrete spectrum of $H$ in the case when $V_0\in L^\infty(\br^d)$ and $V\in L^p(\br^d)$, $p>\max (d/2,1)$.

12 pages, 1 figure. arXiv admin note: text overlap with arXiv:1502.06022

References in corpus (2)

• Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials
• Variation of discrete spectra for non-selfadjoint perturbations of selfadjoint operators