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)



Composition operators induced by functions with supremum strictly smaller than $ 1$

Author: Nina Zorboska
Journal: Proc. Amer. Math. Soc. 106 (1989), 679-684
MSC: Primary 47B38
MathSciNet review: 953015
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We give some partial solutions to the following problem. Does a function analytic in the unit disc $ D$ with supremum strictly smaller than 1 , induce a bounded composition operator on all weighted Hardy spaces $ {H^2}(\beta )$.

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

  • [1] D. M. Boyd, Composition operators on the Bergman space and analytic function spaces on the annulus, Thesis, Univ. of North Carolina, 1974. MR 0407644 (53:11416)
  • [2] C. Cowen, Composition operators on $ {H^2}$, J. Operator Theory 9 (1983), 77-106. MR 695941 (84d:47038)
  • [3] B. D. MacCluer and J. H. Shapiro, Angular derivatives and compact composition operators on the Hardy and Bergman spaces, Canad. J. Math. 38 (1986), 878-907. MR 854144 (87h:47048)
  • [4] E. A. Nordgren, Composition operators in Hilbert spaces, in Hilbert space operators, Lecture Notes in Math., vol. 693, Springer-Verlag, Berlin, Heidelberg, New York, 1977.
  • [5] E. A. Nordgren, P. Rosenthal and F. S. Wintrobe, Invertible composition operators on $ {H^p}$, J. Funct. Anal. 73 (1987), 324-344. MR 899654 (89c:47044)
  • [6] R. Roan, Composition operators on the space of functions with $ {H^p}$ derivative, Houston J. Math. 4 (1978), 423-438. MR 0512878 (58:23735)
  • [7] R. Schatten, Norm ideals of completely continuous operators, Springer-Verlag, Berlin, 1960. MR 0119112 (22:9878)
  • [8] H. J. Schwartz, Composition operators on $ {H^p}$, Thesis, Univ. of Toledo, 1969.
  • [9] J. H. Shapiro, Compact composition operators on spaces of boundary-regular holomorphic functions, Proc. Amer. Math. Soc. 100 (1987), 49-57. MR 883400 (88c:47059)
  • [10] J. H. Shapiro and P. D. Taylor, Compact, nuclear and Hilbert-Schmidt composition operators on $ {H^2}$, Indiana Univ. Math. J. 23 (1973/1974), 471-496. MR 0326472 (48:4816)
  • [11] A. L. Shields, Weighted shift operators and analytic function theory, Topics in Operator Theory, Math Surveys, No. 13, Amer. Math. Soc., Providence, R.I., 1974. MR 0361899 (50:14341)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47B38

Retrieve articles in all journals with MSC: 47B38

Additional Information

Keywords: Composition operator, weighted Hardy spaces, trace class operator
Article copyright: © Copyright 1989 American Mathematical Society

American Mathematical Society