Joint hyponormality of rational Toeplitz pairs (Q1049596)

The authors study joint hyponormality of Toeplitz operators on the Hardy space whose symbols are rational functions in \(L^{\infty}\). In [``Joint hyponormality of Toeplitz pairs'' (Mem.\ Am.\ Math.\ Soc.\ 712) (2001; Zbl 0982.47022)], \textit{R.\,E.\thinspace Curto} and the second author characterized joint hyponormality of pairs of Toeplitz operators with trigonometric polynomial symbols. The main result of this paper is the following Theorem. Let \(\phi\) and \(\psi\) be rational functions in \(L^{\infty}\). If \((T_{\phi}, T_{\psi})\) is jointly hyponormal, then \(\phi-\beta\psi\in H^2\) for some constant \(\beta\).