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On the Complex Symmetric and Skew-Symmetric Operators with a Simple Spectrum
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7
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On the Complex Symmetric and Skew-Symmetric Operators with a Simple Spectrum
Інший ID:
2010 Mathematics Subject Classification: 44A60
DOI:10.3842/SIGMA.2011.016
DOI:10.3842/SIGMA.2011.016
Посилання:
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.
Підтримка:
The author is grateful to referees for their comments and suggestions.
Дата:
2011
Переглядів:
615
Завантажень:
263
Анотація:
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.
