On the Spectrum of Hilbert Matrix Operator

The Hilbert matrix $$\begin{aligned} {\mathcal {H}}_\lambda =\left( \frac{1}{n+m+\lambda }\right) _{n,m=0}^{\infty }, \quad \lambda \ne 0,-1,-2, \ldots \, \end{aligned}$$ generates a bounded linear operator in the Hardy spaces $$H^p$$ and in the $$l^p$$ -spaces. The aim of this paper is to study the spectrum of this operator in the spaces mentioned. In a sense, the presented investigation continues earlier works of various authors. More information concerning the history of the topic can be found in the introduction.