On the Complex Symmetric and Skew-Symmetric Operators with a Simple Spectrum
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
On the Complex Symmetric and Skew-Symmetric Operators with a Simple Spectrum
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| Creator |
Zagorodnyuk, S.M.
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| 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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| Date |
2019-02-11T14:57:30Z
2019-02-11T14:57:30Z 2011 |
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| Type |
Article
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| Identifier |
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 http://dspace.nbuv.gov.ua/handle/123456789/146779 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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