On existence of maximal semidefinite invariant subspaces for J-dissipative operators

2010/07/23 by S. G. Pyatkov, Pyatkov, S. G.
Computer Science · Mathematics · #47D06 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods in inverse problems #Primary 47B50 #Secondary 46C20 #Spectral Theory in Mathematical Physics #math.FA #msc:46C20 #msc:47B50 #msc:47D06

paper · pdf · doi:10.48550/arxiv.1007.4131

22 pages

arxiv created 2010/07/23 · openalex publication_date 2010/07/23 · arxiv updated 2010/07/26 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We describe necessary and sufficient conditions for a J-dissipative operator in a Krein space to have maximal semidefinite invariant subspaces. The semigroup properties of the restrictions of an operator to these subspaces are studied. Applications are given to the case when an operator admits matrix representation with respect to the canonical decomposition of the space. The main conditions are given in the terms of the interpolation theory of Banach spaces.

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