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 | References | Similar Articles | Additional Information
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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- James A. Deddens and Tin Kin Wong, The commutant of analytic Toeplitz operators, Trans. Amer. Math. Soc. 184 (1973), 261–273. MR 324467, DOI https://doi.org/10.1090/S0002-9947-1973-0324467-0
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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/img3.gif" ALT="${H^2}$">,
analytic Toeplitz operator,
commutant
Article copyright:
© Copyright 1975
American Mathematical Society