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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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 \[ A_B(f)(z)=\frac {1}{n}\sum _{B(\xi )=z}f(\xi ).\]
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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