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

2004/12/06 by A. A. Shkalikov, Shkalikov, A. A.
Mathematics · #47A10 #47A15 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:47A10 #msc:47A15

paper · pdf · doi:10.48550/arxiv.math/0412116

11 pages

arxiv created 2004/12/06 · arxiv updated 2009/12/01

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.

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