On the invariant subspace problem for dissipative operators in Krein spaces

2005/12/20 by А. А. Шкаликов, A. A. Shkalikov, Shkalikov, A. A.
Computer Science · Mathematics · #47A15 #47B50 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #math.FA #msc:47A15 #msc:47B50

paper · pdf · doi:10.48550/arxiv.math/0512465

8 pages

openalex publication_date 2005/12/20 · arxiv created 2005/12/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We relax assumptions for a dissipative operator in Krein space to possess a maximal non-negative invariant subspace. Our main result is a generalization of a well-known Pontrjagin-Krein-Langer-Azizov theorem. Then we investigate the semigroup properties of the restriction of the operator onto the invariant subspace.

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