I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
1999, VOLUME 5, NUMBER 2, PAGES 627-635
On the existence of invariant subspaces of dissipative operators
in space with indefinite metric
A. A. Shkalikov
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Let be Hilbert space with fundamental symmetry
where are mutualy
orthogonal projectors such that is identity
The main result of the paper is the following: if
a maximal dissipative operator in the Krein space , the domain of contains , and
is compact, then there exists an -invariant maximal
non-negative subspace such that the spectrum of
the restriction lies in the closed upper-half complex
This theorem is a modification of well-known results of
L. S. Pontrjagin, H. Langer, M. G. Krein and
T. Ja. Azizov.
A new proof is proposed in this paper.
All articles are
published in Russian.
Last modified: July 6, 1999