On operators of transition in Krein spaces
The paper is devoted to investigation of operators of transition and the corresponding decompositions of Krein spaces. The obtained results are applied to the study of relationship between solutions of operator Riccati equations and properties of the associated operator matrix \(L\). In this way, we...
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AGH Univeristy of Science and Technology Press
2011-01-01
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| Series: | Opuscula Mathematica |
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| Online Access: | http://www.opuscula.agh.edu.pl/vol31/1/art/opuscula_math_3104.pdf |
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doaj-90de0e62958248c7a9c553317681f0a52020-11-24T21:03:18ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742011-01-013114959http://dx.doi.org/10.7494/OpMath.2011.31.1.493104On operators of transition in Krein spacesA. Grod0S. Kuzhel1V. Sudilovskaya2Taras Shevchenko National University, 03127, Kyiv, UkraineNational Academy of Sciences of Ukraine, Institute of Mathematics, 01601, Kyiv, UkraineNational Pedagogical Dragomanov University, 01601, Kyiv, UkraineThe paper is devoted to investigation of operators of transition and the corresponding decompositions of Krein spaces. The obtained results are applied to the study of relationship between solutions of operator Riccati equations and properties of the associated operator matrix \(L\). In this way, we complete the known result (see Theorem 5.2 in the paper of S. Albeverio, A. Motovilov, A. Skhalikov, Integral Equ. Oper. Theory 64 (2004), 455-486) and show the equivalence between the existence of a strong solution \(K\) (\(\|K\|\lt 1\)) of the Riccati equation and similarity of the \(J\)-self-adjoint operator \(L\) to a self-adjoint one.http://www.opuscula.agh.edu.pl/vol31/1/art/opuscula_math_3104.pdfKrein spacesindefinite metricsoperator of transitionoperator Riccati equation |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
A. Grod S. Kuzhel V. Sudilovskaya |
| spellingShingle |
A. Grod S. Kuzhel V. Sudilovskaya On operators of transition in Krein spaces Opuscula Mathematica Krein spaces indefinite metrics operator of transition operator Riccati equation |
| author_facet |
A. Grod S. Kuzhel V. Sudilovskaya |
| author_sort |
A. Grod |
| title |
On operators of transition in Krein spaces |
| title_short |
On operators of transition in Krein spaces |
| title_full |
On operators of transition in Krein spaces |
| title_fullStr |
On operators of transition in Krein spaces |
| title_full_unstemmed |
On operators of transition in Krein spaces |
| title_sort |
on operators of transition in krein spaces |
| publisher |
AGH Univeristy of Science and Technology Press |
| series |
Opuscula Mathematica |
| issn |
1232-9274 |
| publishDate |
2011-01-01 |
| description |
The paper is devoted to investigation of operators of transition and the corresponding decompositions of Krein spaces. The obtained results are applied to the study of relationship between solutions of operator Riccati equations and properties of the associated operator matrix \(L\). In this way, we complete the known result (see Theorem 5.2 in the paper of S. Albeverio, A. Motovilov, A. Skhalikov, Integral Equ. Oper. Theory 64 (2004), 455-486) and show the equivalence between the existence of a strong solution \(K\) (\(\|K\|\lt 1\)) of the Riccati equation and similarity of the \(J\)-self-adjoint operator \(L\) to a self-adjoint one. |
| topic |
Krein spaces indefinite metrics operator of transition operator Riccati equation |
| url |
http://www.opuscula.agh.edu.pl/vol31/1/art/opuscula_math_3104.pdf |
| work_keys_str_mv |
AT agrod onoperatorsoftransitioninkreinspaces AT skuzhel onoperatorsoftransitioninkreinspaces AT vsudilovskaya onoperatorsoftransitioninkreinspaces |
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1716773437425319936 |