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Mat. Sb., 2012, Volume 203, Number 2, Pages 87–110 (Mi msb7746)  

This article is cited in 3 scientific papers (total in 3 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

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.

DOI: https://doi.org/10.4213/sm7746

Full text: PDF file (625 kB)
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English version:
Sbornik: Mathematics, 2012, 203:2, 234–256

Bibliographic databases:

UDC: 517.98+517.982.224
MSC: Primary 47B50; Secondary 46C50
Received: 29.05.2010 and 09.04.2011

Citation: S. G. Pyatkov, “On the existence of maximal semidefinite invariant subspaces for $J$-dissipative operators”, Mat. Sb., 203:2 (2012), 87–110; Sb. Math., 203:2 (2012), 234–256

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. G. Wanjala, “The invariant subspace problem for absolutely $p$-summing operators in Krein spaces”, J. Inequal. Appl., 2012 (2012), 254, 13 pp.  crossref  mathscinet  zmath  isi  elib  scopus
    2. T. Ya. Azizov, A. Dijksma, I. V. Gridneva, “Conditional reducibility of certain unbounded nonnegative Hamiltonian operator functions”, Integral Equations Operator Theory, 73:2 (2012), 273–303  crossref  mathscinet  zmath  isi  elib  scopus
    3. S. G. Pyatkov, “Existence of maximal semidefinite invariant subspaces and semigroup properties of some classes of ordinary differential operators”, Oper. Matrices, 8:1 (2014), 237–254  crossref  mathscinet  zmath  isi  elib  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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