Zagorodnyuk, Sergey M. On the complex symmetric and skew-symmetric operators with a simple spectrum. (English) Zbl 1218.44002 SIGMA, Symmetry Integrability Geom. Methods Appl. 7, Paper 016, 9 p. (2011). Summary: 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 the set of all such operators is a proper subset of the 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 \(H\). Cited in 9 Documents MSC: 44A60 Moment problems Keywords:complex symmetric operator; complex skew-symmetric operator; cyclic operator; simple spectrum; Hilbert space PDFBibTeX XMLCite \textit{S. M. Zagorodnyuk}, SIGMA, Symmetry Integrability Geom. Methods Appl. 7, Paper 016, 9 p. (2011; Zbl 1218.44002) Full Text: DOI arXiv EuDML