Document Type
Article
Publication Date
12-1-2010
Publication Title
Integral Equations and Operator Theory
Abstract
For any analytic self-map φ of {z : |z| < 1} we give four separate conditions, each of which is necessary and sufficient for the composition operator Cφ to be closed-range on the Bloch space B . Among these conditions are some that appear in the literature, where we provide new proofs. We further show that if Cφ is closed-range on the Bergman space A2 , then it is closed-range on B , but that the converse of this fails with a vengeance. Our analysis involves an extension of the Julia-Carathéodory Theorem.
Repository Citation
Akeroyd, John R.; Ghatage, Pratibha G.; and Tjani, Maria, "Closed-Range Composition Operators on A2 and the Bloch Space" (2010). Mathematics and Statistics Faculty Publications. 174.
https://engagedscholarship.csuohio.edu/scimath_facpub/174
DOI
10.1007/s00020-010-1806-7
Version
Postprint
Publisher's Statement
The final publication is available at Springer via http://dx.doi.org/10.1007/s00020-010-1806-7
Volume
68
Issue
4
