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POWERS OF COMPOSITION OPERATORS: ASYMPTOTIC BEHAVIOUR ON BERGMAN, DIRICHLET AND BLOCH SPACES

Part of: Entire and meromorphic functions, and related topics Groups and semigroups of linear operators, their generalizations and applications Special classes of linear operators

Published online by Cambridge University Press:  27 November 2019

W. ARENDT ,
I. CHALENDAR ,
M. KUMAR  and
S. SRIVASTAVA
W. ARENDT
Affiliation:
Institute of Applied Analysis, University of Ulm, 89069, Ulm, Germany email wolfgang.arendt@uni-ulm.de
I. CHALENDAR*
Affiliation:
Université Paris-Est, LAMA (UMR 8050), UPEM, UPEC, CNRS, F-77454, Marne-la-Vallée, France email isabelle.chalendar@u-pem.fr
M. KUMAR
Affiliation:
Lady Shri Ram College For Women, Department of Mathematics, University of Delhi, Delhi, India email mahekumar81@gmail.com
S. SRIVASTAVA
Affiliation:
Department of Mathematics, University of Delhi, South Campus, Delhi, India email sachi_srivastava@yahoo.com
*
✉isabelle.chalendar@u-pem.fr
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Abstract

We study the asymptotic behaviour of the powers of a composition operator on various Banach spaces of holomorphic functions on the disc, namely, standard weighted Bergman spaces (finite and infinite order), Bloch space, little Bloch space, Bloch-type space and Dirichlet space. Moreover, we give a complete characterization of those composition operators that are similar to an isometry on these various Banach spaces. We conclude by studying the asymptotic behaviour of semigroups of composition operators on these various Banach spaces.

Keywords

composition operatorsweighted Bergman spacesBloch spaceasymptotic behaviourholomorphic semiflows

MSC classification

Primary: 30D05: Functional equations in the complex domain, iteration and composition of analytic functions
Secondary: 47D03: Groups and semigroups of linear operators 47B33: Composition operators
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 108 , Issue 3 , June 2020 , pp. 289 - 320
Copyright
© 2019 Australian Mathematical Publishing Association Inc.

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