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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Intersections of commutants of analytic Toeplitz operators


Author: James E. Thomson
Journal: Proc. Amer. Math. Soc. 52 (1975), 305-310
MSC: Primary 47B35; Secondary 30A78
MathSciNet review: 0399927
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Abstract: In this paper we study the intersection of commutants of analytic Toeplitz operators. Our main result is that if $ \phi $ is a finite Blaschke product and $ \Psi \epsilon {H^\infty }$, then $ \{ {T_\phi }\} ' \cap \{ {T_\Psi }\} ' = \{ {T_I}\} '$ where $ I$ is a finite Blaschke product and $ \phi $ and $ \Psi $ are functions of $ I$. The key step is a function-theoretic theorem describing the relationship between a finite Blaschke product and any $ {H^\infty }$ function.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0399927-4
PII: S 0002-9939(1975)0399927-4
Keywords: Analytic function, inner function, $ {H^\infty }$, $ {H^2}$, analytic Toeplitz operator, commutant
Article copyright: © Copyright 1975 American Mathematical Society