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 on a Hilbert space is said to have the transitive algebra property if is the only transitive operator algebra which contains . 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