Perturbations of the unilateral shift and transitive operator algebras
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- by Mohamad A. Ansari PDF
- Proc. Amer. Math. Soc. 101 (1987), 455-461 Request permission
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.References
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Additional Information
- © Copyright 1987 American Mathematical Society
- 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