Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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


References [Enhancements On Off] (What's this?)

  • 1. C.C. Cowen and B.D. MacCluer, Composition Operators on Spaces of Analytic Functions, CRC Press, Boca Raton (1995). MR 97i:47056
  • 2. C.C. Cowen and B.D. MacCluer, Some Problems on Composition Operators, Contemporary Mathematics No. 213, American Mathematical Society (1998), pp17-25. MR 99d:47029
  • 3. J. N. Mc Donald, Some operators on $L^2(dm)$associated with finite Blaschke products, Lecture Notes in Mathematics, No.693, Springer-Verlag, New York (1978), pp124-132. MR 81c:47033
  • 4. E. A. Nordgren, Composition operators, Canadian J. of Math. 20(1968), pp442-449. MR 36:6961
  • 5. R. Rochberg, Linear maps of the disk algebra, Pacific J. Math. 44 (1973), pp337-354. MR 47:4003
  • 6. J.V. Ryff, Subordinate $H\sp{p}$ functions, Duke Math. J. 33 (1966) pp347-354. MR 33:289

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47B33, 46E20

Retrieve articles in all journals with MSC (2000): 47B33, 46E20

Additional Information

John N. Mc Donald
Affiliation: Department of Mathematics, Arizona State University, Tempe, Arizona 85287-1804

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

American Mathematical Society