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Journal of Operator Theory

Volume 86, Issue 1, Summer 2021  pp. 189-201.

Weighted composition operators: isometries and asymptotic behaviour

Authors:  Isabelle Chalendar (1), Jonathan R. Partington (2)
Author institution: (1) LAMA, Universite Gustave Eiffel, Universite Paris Est Creteil, CNRS, F-77454 Marne-la-Vallee, France
(2) School of Mathematics, University of Leeds, Leeds LS2 9JT, U.K.

Summary: This paper studies the behaviour of iterates of weigh\-ted composition operators acting on spaces of analytic functions, with particular emphasis on the Hardy space $H^2$. Questions relating to uniform, strong and weak convergence are resolved in many cases. Connected to this is the question when a weighted composition operator is an isometry, and new results are given in the case of the Hardy and Bergman spaces.

Keywords: weighted composition operator, iteration, isometry

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