The abstract Birman-Schwinger principle and spectral stability

Abstract

We discuss abstract Birman-Schwinger principles to study spectra of self-adjoint operators subject to small non-self-adjoint perturbations in a factorised form. In particular, we extend and in part improve a classical result by Kato which ensures spectral stability. As an application, we revisit known results for Schr\"odinger and Dirac operators in Euclidean spaces and establish new results for Schr\"odinger operators in three-dimensional hyperbolic space.