On the reflexivity of operators on function spaces

Abstract

Let Ω \Omega be a bounded plane domain. Sufficient conditions are given so that an operator T T in the Cowen-Douglas class B n ( Ω ) {\mathcal {B}_n}(\Omega ) is reflexive. The operator M z {M_z} of multiplication by z z on a Hilbert space of functions analytic on a finitely connected domain Ω \Omega is shown to be reflexive whenever σ ( M z ) = Ω ¯ \sigma ({M_z}) = \overline \Omega is a spectral set.