The commutants of certain analytic Toeplitz operators
Author:
James E. Thomson
Journal:
Proc. Amer. Math. Soc. 54 (1976), 165-169
DOI:
https://doi.org/10.1090/S0002-9939-1976-0388156-7
MathSciNet review:
0388156
Full-text PDF Free Access
Abstract | References | Additional Information
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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Additional Information
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
