Archiv der Mathematik

, Volume 110, Issue 5, pp 487–500 | Cite as

Convergence of powers of composition operators on certain spaces of holomorphic functions defined on the right half plane

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Abstract

This paper studies the asymptotic behaviour of the powers \(C_\varphi ^n\) of a composition operator \(C_\varphi \) on certain spaces of holomorphic functions defined on the right half plane \(\mathbb {C}_+\). It is shown that for composition operators on the Hardy spaces and the standard weighted Bergman spaces, if the inducing map \(\varphi \) is not of parabolic type, then either the powers \(C_\varphi ^n\) converge uniformly only to 0 or they do not converge even strongly.

Keywords

Composition operators Banach spaces of holomorphic functions on the half plane Asymptotics. 

Mathematics Subject Classification

47B33 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of DelhiDelhiIndia
  2. 2.Lady Shri Ram College, Department of MathematicsUniversity of DelhiDelhiIndia

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