Generalized wave operators in space with an indefinite metric (Q1122118)

For a pair of selfadjoint operators \(A_ 1\), \(A_ 2\) on a Krein space the wave operator \(W_{\pm}=s-\lim_{t\to \pm \infty}W(t)P_ 1\) is defined as in a Hilbert space, where \(W(t)=e^{itA_ 2}e^{-itA_ 1}\) and \(P_ 1\) is the projection to the absolutely continuous subspace of \(A_ 1\). Under some condition existence of the wave operator is proved. For instance, if \(A_ 2\) is a trace class perturbation of \(A_ 1\) then the wave operator exists. Invariance is also discussed.