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Fundamentalnaya i Prikladnaya Matematika, 1999, Volume 5, Issue 2, Pages 627–635
(Mi fpm397)
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This article is cited in 4 scientific papers (total in 4 papers)
On the existence of invariant subspaces of dissipative operators in space with indefinite metric
A. A. Shkalikov M. V. Lomonosov Moscow State University
Abstract:
Let $\mathcal H$ be Hilbert space with fundamental symmetry $J=P_+-P_-$, where $P_\pm$ are mutualy orthogonal projectors such that $J^2$ is identity operator. The main result of the paper is the following: if $A$ is a maximal dissipative operator in the Krein space $\mathcal K=\{\mathcal H,J\}$, the domain of $A$ contains $P_+(\mathcal H)$, and the operator $P_+AP_-$ is compact, then there exists an $A$-invariant maximal non-negative subspace $\mathcal L$ such that the spectrum of the restriction $A|_{\mathcal L}$ lies in the closed upper-half complex plain. 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.
Received: 01.03.1999
Citation:
A. A. Shkalikov, “On the existence of invariant subspaces of dissipative operators in space with indefinite metric”, Fundam. Prikl. Mat., 5:2 (1999), 627–635
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https://www.mathnet.ru/eng/fpm397 https://www.mathnet.ru/eng/fpm/v5/i2/p627
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Abstract page: | 415 | Full-text PDF : | 172 | First page: | 2 |
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