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Proceedings of the American Mathematical Society

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



The commutants of certain analytic Toeplitz operators

Author: James E. Thomson
Journal: Proc. Amer. Math. Soc. 54 (1976), 165-169
MathSciNet review: 0388156
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Abstract: In this paper we characterize the commutants of two classes of analytic Toeplitz operators. We show that if $F$ in ${H^\infty }$ is univalent and nonvanishing, the $\{ {T_{{F^2}}}\} ’ = \{ {T_z}\} ’$. When $\varphi$ is the product of two Blaschke factors, we characterize $\{ {T_\varphi }\} ’$ in terms of algebraic combinations of Toeplitz and composition operators.

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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/img9.gif" ALT="${H^2}$">, analytic Toeplitz operator, commutant
Article copyright: © Copyright 1976 American Mathematical Society