A generalization of Hankel operators (Q1604627)

The author studies so called \(\lambda\)-Hankel operators which are the solutions of the operator equation \(S^\ast X-XS=\lambda X\) where \(\lambda\) is a complex number and \(S\) is the unilateral forward shift. He investigates some of the properties of \(\lambda\)-Hankel operators such as: invertibility, spectra, finite rank and positivity. Some other operator equations involving \(S\) are also considered.