On the Complex Symmetric and Skew-Symmetric Operators with a Simple Spectrum
In this paper we obtain necessary and sufficient conditions for a linear bounded operator in a Hilbert space H to have a three-diagonal complex symmetric matrix with non-zero elements on the first sub-diagonal in an orthonormal basis in H. It is shown that a set of all such operators is a proper sub...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2011 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2011
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146779 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On the Complex Symmetric and Skew-Symmetric Operators with a Simple Spectrum / S.M. Zagorodnyuk // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 10 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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Zagorodnyuk, S.M. 2019-02-11T14:57:30Z 2019-02-11T14:57:30Z 2011 On the Complex Symmetric and Skew-Symmetric Operators with a Simple Spectrum / S.M. Zagorodnyuk // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 10 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 44A60 DOI:10.3842/SIGMA.2011.016 https://nasplib.isofts.kiev.ua/handle/123456789/146779 In this paper we obtain necessary and sufficient conditions for a linear bounded operator in a Hilbert space H to have a three-diagonal complex symmetric matrix with non-zero elements on the first sub-diagonal in an orthonormal basis in H. It is shown that a set of all such operators is a proper subset of a set of all complex symmetric operators with a simple spectrum. Similar necessary and sufficient conditions are obtained for a linear bounded operator in H to have a three-diagonal complex skew-symmetric matrix with non-zero elements on the first sub-diagonal in an orthonormal basis in H. The author is grateful to referees for their comments and suggestions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On the Complex Symmetric and Skew-Symmetric Operators with a Simple Spectrum Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
On the Complex Symmetric and Skew-Symmetric Operators with a Simple Spectrum |
| spellingShingle |
On the Complex Symmetric and Skew-Symmetric Operators with a Simple Spectrum Zagorodnyuk, S.M. |
| title_short |
On the Complex Symmetric and Skew-Symmetric Operators with a Simple Spectrum |
| title_full |
On the Complex Symmetric and Skew-Symmetric Operators with a Simple Spectrum |
| title_fullStr |
On the Complex Symmetric and Skew-Symmetric Operators with a Simple Spectrum |
| title_full_unstemmed |
On the Complex Symmetric and Skew-Symmetric Operators with a Simple Spectrum |
| title_sort |
on the complex symmetric and skew-symmetric operators with a simple spectrum |
| author |
Zagorodnyuk, S.M. |
| author_facet |
Zagorodnyuk, S.M. |
| publishDate |
2011 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
In this paper we obtain necessary and sufficient conditions for a linear bounded operator in a Hilbert space H to have a three-diagonal complex symmetric matrix with non-zero elements on the first sub-diagonal in an orthonormal basis in H. It is shown that a set of all such operators is a proper subset of a set of all complex symmetric operators with a simple spectrum. Similar necessary and sufficient conditions are obtained for a linear bounded operator in H to have a three-diagonal complex skew-symmetric matrix with non-zero elements on the first sub-diagonal in an orthonormal basis in H.
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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/146779 |
| citation_txt |
On the Complex Symmetric and Skew-Symmetric Operators with a Simple Spectrum / S.M. Zagorodnyuk // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 10 назв. — англ. |
| work_keys_str_mv |
AT zagorodnyuksm onthecomplexsymmetricandskewsymmetricoperatorswithasimplespectrum |
| first_indexed |
2025-12-07T15:37:53Z |
| last_indexed |
2025-12-07T15:37:53Z |
| _version_ |
1850864433696342016 |