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Proceedings of the American Mathematical Society

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On the reflexivity of operators on function spaces


Authors: K. Seddighi and B. Yousefi
Journal: Proc. Amer. Math. Soc. 116 (1992), 45-52
MSC: Primary 47B38; Secondary 47A15, 47B37
MathSciNet review: 1104402
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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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DOI: https://doi.org/10.1090/S0002-9939-1992-1104402-5
Keywords: Reflexive, spectral set, Hilbert space of analytic functions, bilateral weighted shift
Article copyright: © Copyright 1992 American Mathematical Society