The Spectral Shift Function for Certain Block Operator Matrices

Abstract

Let L0 be a 2 × 2 diagonal self-adjoint block operator matrix with entries A and D. If operators B and B* are added to the off diagonal zeros, certain parts of the spectrum of L0 move to the right and other parts move to the left. In this paper it is shown that, correspondingly, if B is a trace class operator M. G. Krein's spectral shift function is of constant sign on certain intervals.