On invariant subspaces of dissipative operators in a space with indefinite metric

Abstract

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