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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
DOI: https://doi.org/10.1090/S0002-9939-1975-0399927-4
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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Keywords: Analytic function, inner function, <!– MATH ${H^\infty }$ –> <IMG WIDTH="41" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="${H^\infty }$">, <IMG WIDTH="33" HEIGHT="23" ALIGN="BOTTOM" BORDER="0" SRC="images/img3.gif" ALT="${H^2}$">, analytic Toeplitz operator, commutant
Article copyright: © Copyright 1975 American Mathematical Society