Multiplication operators on Hilbert spaces of analytic functions

Abstract.

Let $\mathcal{H}$ be a Hilbert space of functions analytic on a plane domain Ω such that for every λ in Ω the functional of evaluation at λ is bounded. Assume further that $\mathcal{H}$ contains the constants and admits multiplication by the independent variable z, M _z , as a bounded operator. We give sufficient conditions for M _z to be reflexive.