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Full-Text Articles in Physical Sciences and Mathematics
Closed-Range Composition Operators On A2 And The Bloch Space, John R. Akeroyd, Pratibha G. Ghatage, Maria Tjani
Closed-Range Composition Operators On A2 And The Bloch Space, John R. Akeroyd, Pratibha G. Ghatage, Maria Tjani
Mathematics and Statistics Faculty Publications
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.