Commutant of analytic Toeplitz operators on the Bergman space (Q627554)

The authors study the commutant of Toeplitz operators with polynomial symbols acting on the standard weighted Bergman space on the unit disk. Let \(\rho_F(T_p)\) denote the Fredholm domain of \(T_p\), \(\sigma(T_p)\) denote the spectrum of \(T_p\), and let \(\mathcal{A}'(T_p)\) denote the commutant of \(T_p\). The main result of the paper states that, given a polynomial \(p(z)\), \(\mathcal{A}'(T_p) = \mathcal{A}'(T_{z^l})\), where \(l=\min\{|\mathrm{index}(T_p - \lambda)| : \lambda \in \rho_F(T_p) \cap \sigma(T_p) \}\).