The abstract Birman—Schwinger principle and spectral stability

We discuss abstract Birman—Schwinger principles to study spectra of self-adjoint operators subject small non-self-adjoint perturbations in a factorised form. In particular, we extend and part improve classical result by Kato which ensures that the spectrum does not change under perturbations. As an application, revisit known results for Schrödinger Dirac Euclidean spaces establish new three-dimensional hyperbolic space.