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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2011 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2011
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/146779 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862673099116249088 |
|---|---|
| author | Zagorodnyuk, S.M. |
| author_facet | Zagorodnyuk, S.M. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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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| first_indexed | 2025-12-07T15:37:53Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146779 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T15:37:53Z |
| publishDate | 2011 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | On the Complex Symmetric and Skew-Symmetric Operators with a Simple Spectrum Zagorodnyuk, S.M. |
| title | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146779 |
| work_keys_str_mv | AT zagorodnyuksm onthecomplexsymmetricandskewsymmetricoperatorswithasimplespectrum |