Adjoints of a class of composition operators
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- by John N. Mc Donald PDF
- Proc. Amer. Math. Soc. 131 (2003), 601-606 Request permission
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 \[ A_B(f)(z)=\frac {1}{n}\sum _{B(\xi )=z}f(\xi ).\]References
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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
- 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
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 601-606
- MSC (2000): Primary 47B33; Secondary 46E20
- DOI: https://doi.org/10.1090/S0002-9939-02-06590-5
- MathSciNet review: 1933352