Hyponormality of Toeplitz operators with polynomial symbols: An extremal case (Q2770424)

The authors prove a necessary and sufficient condition in order for a Toeplitz operator with polynomial symbol \(\varphi=\overline{g}+f\) (such that \(g\) divides \(f\)), acting on the Hardy space \(H^2(\mathbb{T})\), to be hyponormal. More precisely, they analyze the case when NEWLINE\[NEWLINE\biggl|\sum_{\zeta\in \mathbb{Z}(\psi)}\zeta\biggr|= |\mu|-\frac{1}{|\mu|},NEWLINE\]NEWLINE where \(\psi=f/g\), \(\mu\) is the leading coefficient of \(\psi\) and \(\mathbb{Z}(\psi)\) is the set of the zeros of \(\psi\).