Lukas Schimmer (Imperial) - "Lieb-Thirring inequalities for perturbations of the continuous spectrum of the Laplacian"

Abstract

Lieb-Thirring inequalities provide a bound for the negative eigenvalues of a Schrödinger operator in terms of the potential. In this talk, we will present the main ideas behind recent results of R. Frank, M. Lewin, E. Lieb and R. Seiringer who discuss analogous inequalities for perturbations of the continuous spectrum of the Laplace operator by local potentials. In order to do this, we will introduce a more general definition of the trace for operators which are not necessarily trace class.