Geodesic
On the Complex Symmetric and Skew-Symmetric Operators with a Simple Spectrum
Symmetry, integrability and geometry: methods and applications, Tome 7 (2011) Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $H$.
Keywords: complex symmetric operator; complex skew-symmetric operator; cyclic operator; simple spectrum. 
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     title = {On the {Complex} {Symmetric} and {Skew-Symmetric} {Operators} with {a~Simple} {Spectrum}},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a15/}
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Sergey M. Zagorodnyuk. On the Complex Symmetric and Skew-Symmetric Operators with a Simple Spectrum. Symmetry, integrability and geometry: methods and applications, Tome 7 (2011). http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a15/

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