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Sbornik: Mathematics, 2012, Volume 203, Issue 2, Pages 234–256
DOI: https://doi.org/10.1070/SM2012v203n02ABEH004221 (Mi sm7746) 		 
This article is cited in 5 scientific papers (total in 5 papers)

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

S. G. Pyatkovab

a Ugra State University, Khanty-Mansiysk
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
English version PDF (540 kB) Citations (5) Russian version article
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DOI: https://doi.org/10.1070/SM2012v203n02ABEH004221
Abstract: For a certain class of operators we present some necessary and sufficient conditions for a $J$-dissipative operator in a Kreǐn space to have maximal semidefinite invariant subspaces. We investigate the semigroup properties of restrictions of the operator to these invariant subspaces. These results are applied to the case when the operator admits a matrix representation with respect to the canonical decomposition of the space. The main conditions are formulated in terms of interpolation theory for Banach spaces.
Bibliography: 25 titles.
Keywords: dissipative operator, Pontryagin space, Kreǐn space, invariant subspace, analytic semigroup.
Received: 29.05.2010 and 09.04.2011
Bibliographic databases:
Document Type: Article
UDC: 517.98+517.982.224
MSC: Primary 47B50; Secondary 46C50
Language: English
Original paper language: Russian
Citation: S. G. Pyatkov, “On the existence of maximal semidefinite invariant subspaces for $J$-dissipative operators”, Sb. Math., 203:2 (2012), 234–256
Citation in format AMSBIB
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\paper On the existence of maximal semidefinite invariant subspaces for $J$-dissipative operators
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\yr 2012
\vol 203
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\pages 234--256
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  • https://www.mathnet.ru/eng/sm/v203/i2/p87
    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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