The spectral shift function for certain block operator matrices

Let L-0 be a 2 x 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 L-0 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.