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Sampling sets and closed range composition operators on the Bloch space
Author(s):
Pratibha
Ghatage;
Dechao
Zheng;
Nina
Zorboska
Journal:
Proc. Amer. Math. Soc.
133
(2005),
1371-1377.
MSC (2000):
Primary 47B33
Posted:
October 28, 2004
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Abstract:
We give a necessary and sufficient condition for a composition operator on the Bloch space to have closed range. We show that when is univalent, it is sufficient to consider the action of on the set of Möbius transforms. In this case the closed range property is equivalent to a specific sampling set satisfying the reverse Carleson condition.
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Additional Information:
Pratibha
Ghatage
Affiliation:
Department of Mathematics, Cleveland State University, Cleveland, Ohio 44115
Email:
pghatge@csuohio.edu
Dechao
Zheng
Affiliation:
Department of Mathematics, Vanderbilt University, Nashville, Tennessee 32740
Email:
zheng@math.vanderbilt.edu
Nina
Zorboska
Affiliation:
Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada R3T2N2
Email:
zorboska@cc.umanitoba.CA
DOI:
10.1090/S0002-9939-04-07646-4
PII:
S 0002-9939(04)07646-4
Received by editor(s):
November 7, 2003
Received by editor(s) in revised form:
December 30, 2003
Posted:
October 28, 2004
Dedicated:
Dedicated to Chandler Davis for his 75th birthday
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2004,
American Mathematical Society
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