On the Complex Symmetric and Skew-Symmetric Operators with a Simple Spectrum

• Опубліковано в: : Symmetry, Integrability and Geometry: Methods and Applications
• Дата: 2011
• Автор: Zagorodnyuk, S.M.
• Формат: Стаття
• Мова: Англійська
• Опубліковано: Інститут математики НАН України 2011
• Онлайн доступ: https://nasplib.isofts.kiev.ua/handle/123456789/146779
• 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.

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...