Jan Nesemann studies relatively bounded perturbations of self-adjoint operators in Krein spaces with real spectrum. The main results provide conditions which guarantee the spectrum of the perturbed operator to remain real. Similar results are established for relatively form-bounded perturbations and for pseudo-Friedrichs extensions. The author pays particular attention to the case when the unperturbed self-adjoint operator has infinitely many spectral gaps, either between eigenvalues or, more generally, between separated parts of the spectrum.

Dr. Jan Nesemann holds a master's degree in mathematics as well as in business administration. He received his PhD in mathematics from the University of Bern under the guidance of Prof. Dr. Christiane Tretter. Currently he works as an actuarial and financial services consultant in Zurich.

Linear Operators in Krein Spaces ? PT-Symmetry ? Spectral Theory ? Relatively Bounded/Compact Perturbations ? Relatively Form-Bounded/Form-Compact Perturbations ? Schrödinger Operators