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

Abstract

For a certain class of operators we present some necessary and sufficient conditions for a J-dissipative operator in a Krein 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.

Authors:
 [1]
  1. Ugra State University, Khanty-Mansiysk (Russian Federation)
Publication Date:
OSTI Identifier:
21612785
Resource Type:
Journal Article
Journal Name:
Sbornik. Mathematics
Additional Journal Information:
Journal Volume: 203; Journal Issue: 2; Other Information: DOI: 10.1070/SM2012v203n02ABEH004221; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1064-5616
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; BANACH SPACE; INTERPOLATION; MATHEMATICAL LOGIC; MATHEMATICAL OPERATORS; MATRICES; MATHEMATICAL SOLUTIONS; MATHEMATICAL SPACE; NUMERICAL SOLUTION; SPACE

Citation Formats

Pyatkov, Sergey G. On the existence of maximal semidefinite invariant subspaces for J-dissipative operators. United States: N. p., 2012. Web. doi:10.1070/SM2012V203N02ABEH004221; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
Pyatkov, Sergey G. On the existence of maximal semidefinite invariant subspaces for J-dissipative operators. United States. https://doi.org/10.1070/SM2012V203N02ABEH004221; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)
Pyatkov, Sergey G. 2012. "On the existence of maximal semidefinite invariant subspaces for J-dissipative operators". United States. https://doi.org/10.1070/SM2012V203N02ABEH004221; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
@article{osti_21612785,
title = {On the existence of maximal semidefinite invariant subspaces for J-dissipative operators},
author = {Pyatkov, Sergey G},
abstractNote = {For a certain class of operators we present some necessary and sufficient conditions for a J-dissipative operator in a Krein 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.},
doi = {10.1070/SM2012V203N02ABEH004221; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)},
url = {https://www.osti.gov/biblio/21612785}, journal = {Sbornik. Mathematics},
issn = {1064-5616},
number = 2,
volume = 203,
place = {United States},
year = {Tue Feb 28 00:00:00 EST 2012},
month = {Tue Feb 28 00:00:00 EST 2012}
}