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Composition operators with closed range on the Bloch space


Authors: Pratibha Ghatage, Jun Yan and Dechao Zheng
Journal: Proc. Amer. Math. Soc. 129 (2001), 2039-2044
MSC (2000): Primary 46E15
DOI: https://doi.org/10.1090/S0002-9939-00-05771-3
Published electronically: November 30, 2000
MathSciNet review: 1825915
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Abstract | References | Similar Articles | Additional Information

Abstract:

In this note we investigate conditions under which a holomorphic self-map of the unit disk induces a composition operator with closed range on the Bloch space.


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

  • 1. J. Garnett, Bounded Analytic Functions, Academic Press, New York, 1981. MR 83g:30037
  • 2. K. Madigan and A. Matheson, Compact Composition operators on the Bloch space, Trans. Amer. Math. Soc. 347(1995). 2679-2687. MR 95i:47061
  • 3. J. Shapiro, Composition Operators and Classical Function Theory. Spring-Verlag, New York, 1993. MR 94k:47049
  • 4. W. Smith, Composition operators between Bergman and Hardy spaces, Trans. Amer. Math. Soc. 348(1996), 2331-2348. MR 96i:47056

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Additional Information

Pratibha Ghatage
Affiliation: Department of Mathematics, Cleveland State University, Cleveland, Ohio 44115
Email: ghatage@math.csuohio.edu

Jun Yan
Affiliation: Department of Mathematics, Chongqing University, Chongqing, People’s Republic of China

Dechao Zheng
Affiliation: Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240
Email: zheng@math.vanderbilt.edu

DOI: https://doi.org/10.1090/S0002-9939-00-05771-3
Received by editor(s): May 25, 1999
Received by editor(s) in revised form: November 12, 1999
Published electronically: November 30, 2000
Additional Notes: Supported in part by the National Science Foundation and University Research Council of Vanderbilt University.
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2000 American Mathematical Society

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