Multiplication operators on Hilbert spaces of analytic functions
Let \(H\) be a Hilbert space of functions analytic on a plane domain \(\Omega\). The \(\mathbb C\)-hull of \(\Omega\) is denoted by \(\Omega^*\) and denote by \(\Omega_1\) the component of \(\Omega^*\) containing \(\Omega\). A complex-valued function \(\varphi\) on \(\Omega\) for which \(\varphi f\in H\) for every \(f\in H\) is called a multiplier of \(H\) and the collection of all these multipliers is denoted by \(M(H)\). Assume that each point of \(\Omega\) is a bounded point evaluation and that \(H\) contains the constant functions and \(z\in M(H)\). The author proves that if \(\{e_{\lambda}:\lambda\in\Omega\}\) is norm bounded and \(H^{\infty}(\Omega_1)\subset M(H)\), then \(M_z\) is reflexive.
scientific article; zbMATH DE number 2130598