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Composition operators between weighted Banach spaces of analytic functions

Part of: Linear function spaces and their duals Special classes of linear operators

Published online by Cambridge University Press:  09 April 2009

J. Bonet ,
P. Domański ,
M. Lindström  and
J. Taskinen
J. Bonet
Affiliation:
Dept. Matemática Aplicada Univ. Politécnica de ValenciaE-46071 ValenciaSpain e-mail: jbonet@pleiades.upv.es
P. Domański
Affiliation:
Faculty of Matematics and Comp. Sci. A. Mickiewicz University, ul. Matejki 48/49 60-769 PoznańPoland e-mail: domanski@math.amu.edu.pl
M. Lindström
Affiliation:
Department of Mathematics Åbo Akademi University, FIN-20500 ÅboFinland e-mail: mlindstr@ra.abo.fi
J. Taskinen
Affiliation:
Department of Mathematics P. O. Box 4, FIN-00014University of HelsinkiFinland e-mail: taskinen@cc.helsinki.fi
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Abstract

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We characterize those analytic self-maps ϕ of the unit disc which generate bounded or compact composition operators Cϕ between given weighted Banach spaces H∞v or H0v of analytic functions with the weighted sup-norms. We characterize also those composition operators which are bounded or compact with respect to all reasonable weights v.

MSC classification

Secondary: 47B38: Operators on function spaces (general) 46E15: Banach spaces of continuous, differentiable or analytic functions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 64 , Issue 1 , February 1998 , pp. 101 - 118
Copyright
Copyright © Australian Mathematical Society 1998

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