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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Intersections of commutants of analytic Toeplitz operators
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by James E. Thomson PDF
Proc. Amer. Math. Soc. 52 (1975), 305-310 Request permission

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
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 52 (1975), 305-310
  • MSC: Primary 47B35; Secondary 30A78
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0399927-4
  • MathSciNet review: 0399927