On the reflexivity of operators on function spaces

Seddighi, K.; Yousefi, B.

doi:10.1090/S0002-9939-1992-1104402-5

On the reflexivity of operators on function spaces
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by K. Seddighi and B. Yousefi PDF

Proc. Amer. Math. Soc. 116 (1992), 45-52 Request permission

Abstract:

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

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