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Characterisation of the isometric composition operators on the Bloch space

Published online by Cambridge University Press:  17 April 2009

Flavia Colonna
Flavia Colonna
Affiliation:
Department of Mathematics, George Mason University, Fairfax, VA 22030–4444, United States of America e-mail: fcolonna@gmu.edu
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In this paper, we characterise the analytic functions ϕ mapping the open unit disk ▵ into itself whose induced composition operator Cϕ: f ↦ f ∘ ϕ is an isometry on the Bloch space. We show that such functions are either rotations of the identity function or have a factorisation ϕ = gB where g is a non-vanishing analytic function from Δ into the closure of ▵, and B is an infinite Blaschke product whose zeros form a sequence{zn} containing 0 and a subsequence satisfying the conditions , and

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 72 , Issue 2 , October 2005 , pp. 283 - 290
Copyright
Copyright © Australian Mathematical Society 2005

References

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