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Proceedings of the American Mathematical Society

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Perturbations of the unilateral shift and transitive operator algebras


Author: Mohamad A. Ansari
Journal: Proc. Amer. Math. Soc. 101 (1987), 455-461
MSC: Primary 47C05; Secondary 47B37, 47D25
DOI: https://doi.org/10.1090/S0002-9939-1987-0908648-6
MathSciNet review: 908648
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Abstract: An operator $ T$ on a Hilbert space $ \mathcal{H}$ is said to have the transitive algebra property if $ \mathcal{L}(\mathcal{H})$ is the only transitive operator algebra which contains $ T$. It was shown by Arveson that the unilateral shift has this property. It is the purpose of the present paper to show that perturbations of the unilateral shift by a large class of finite rank operators have the transitive algebra property. Our results are partial solutions of the well-known transitive algebra problem.


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DOI: https://doi.org/10.1090/S0002-9939-1987-0908648-6
Article copyright: © Copyright 1987 American Mathematical Society

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