COMPOSITION OPERATORS WITH CLOSED RANGE ON THE BLOCH SPACE (original) (raw)
2000
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.
Related papers
Closed-Range Composition Operators on and the Bloch Space
Integral Equations and Operator Theory, 2010
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 A, 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. Mathematics Subject Classification (2010). Primary 47B33, 47B38; Secondary 30D55.
Closed-Range Composition Operators on A2 and the Bloch Space
2010
For any analytic self-map φ of {z : |z| \u3c 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
Isometries of the Bloch space among the composition operators
Bulletin of the London Mathematical Society, 2006
ABSTRACT We characterize all isometries among the composition operators acting on the Bloch space in terms of the hyperbolic derivative and cluster set of the symbol, and display a class of nontrivial examples.
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.