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Sampling sets and closed range composition operators on the Bloch space

Authors: Pratibha Ghatage, Dechao Zheng and Nina Zorboska
Journal: Proc. Amer. Math. Soc. 133 (2005), 1371-1377
MSC (2000): Primary 47B33
Published electronically: October 28, 2004
MathSciNet review: 2111961
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Abstract: We give a necessary and sufficient condition for a composition operator $C_{\phi }$ on the Bloch space to have closed range. We show that when $\phi $ is univalent, it is sufficient to consider the action of $C_{\phi }$ 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

Dechao Zheng
Affiliation: Department of Mathematics, Vanderbilt University, Nashville, Tennessee 32740

Nina Zorboska
Affiliation: Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada R3T2N2
Email: zorboska@cc.umanitoba.CA

Received by editor(s): November 7, 2003
Received by editor(s) in revised form: December 30, 2003
Published electronically: October 28, 2004
Dedicated: Dedicated to Chandler Davis for his 75th birthday
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2004 American Mathematical Society

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