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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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
DOI: https://doi.org/10.1090/S0002-9939-1992-1104402-5
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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Keywords: Reflexive, spectral set, Hilbert space of analytic functions, bilateral weighted shift
Article copyright: © Copyright 1992 American Mathematical Society