Invariant Subspaces of Dissipative Operators in a Space with Indefinite Metric

A theorem on the existence of maximal nonnegative invariant subspaces is proved for a special class of dissipative operators in a Hilbert space with indefinite inner product. It is shown that the spectra of the restrictions of these operators on the corresponding invariant subspaces lie in the closed upper half-plane. The theorem obtained is a generalization of the well-known results of L. S. Pontryagin, H. K. Langer, M. G. Krein, and T. Ya. Azizov devoted to this subject.