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Proceedings of the American Mathematical Society

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

 

 

Every isometry is reflexive


Author: James A. Deddens
Journal: Proc. Amer. Math. Soc. 28 (1971), 509-512
MSC: Primary 47.35
MathSciNet review: 0278099
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Abstract: A bounded linear operator $ A$ on a Hilbert space $ \mathcal{H}$ is called reflexive if any bounded linear operator which leaves invariant the invariant subspaces of $ A$ is a limit of polynomials in $ A$ in the weak operator topology. In this note we prove that every isometry $ V$ on a Hilbert space $ \mathcal{H}$ is reflexive.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0278099-7
Keywords: Weakly closed unstarred operator algebras, invariant and reducing subspaces, absolutely continuous and singular unitary operators, unilateral and bilateral shifts
Article copyright: © Copyright 1971 American Mathematical Society