Geodesic
Invariant Subspaces of Dissipative Operators in a~Space with Indefinite Metric
Informatics and Automation, Studies on function theory and differential equations, Tome 248 (2005), pp. 294-303.

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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. 
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A. A. Shkalikov. Invariant Subspaces of Dissipative Operators in a~Space with Indefinite Metric. Informatics and Automation, Studies on function theory and differential equations, Tome 248 (2005), pp. 294-303. http://geodesic.mathdoc.fr/item/TRSPY_2005_248_a26/

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