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Composition operators with closed range on the Bloch space
Author(s):
Pratibha
Ghatage;
Jun
Yan;
Dechao
Zheng
Journal:
Proc. Amer. Math. Soc.
129
(2001),
2039-2044.
MSC (2000):
Primary 46E15
Posted:
November 30, 2000
MathSciNet review:
1825915
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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:
-
- 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:
10.1090/S0002-9939-00-05771-3
PII:
S 0002-9939(00)05771-3
Received by editor(s):
May 25, 1999
Received by editor(s) in revised form:
November 12, 1999
Posted:
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
Copyright of article:
Copyright
2000,
American Mathematical Society
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