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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Adjoints of a class of composition operators


Author: John N. Mc Donald
Journal: Proc. Amer. Math. Soc. 131 (2003), 601-606
MSC (2000): Primary 47B33; Secondary 46E20
Published electronically: June 5, 2002
MathSciNet review: 1933352
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Abstract: Adjoints of certain operators of composition type are calculated. Specifically, on the classical Hardy space $H_2(D)$ of the open unit disk $D$operators of the form $C_B(f)=f\circ B$ are considered, where $B$ is a finite Blaschke product. $C_B^*$ is obtained as a finite linear combination of operators of the form $T_gA_BT_h,$ where $g$ and $h$ are rational functions, $T_g,T_h$ are associated Toeplitz operators and $A_B$ is defined by

\begin{displaymath}A_B(f)(z)=\frac{1}{n}\sum_{B(\xi)=z}f(\xi).\end{displaymath}


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Additional Information

John N. Mc Donald
Affiliation: Department of Mathematics, Arizona State University, Tempe, Arizona 85287-1804
Email: mcdonald@math.la.asu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06590-5
PII: S 0002-9939(02)06590-5
Keywords: Composition operator, adjoint
Received by editor(s): July 18, 2001
Received by editor(s) in revised form: October 5, 2001
Published electronically: June 5, 2002
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2002 American Mathematical Society