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Essential Norm and Weak Compactness of Composition Operators on Weighted Banach Spaces of Analytic Functions

Published online by Cambridge University Press:  20 November 2018

José Bonet ,
Paweł Dománski  and
Mikael Lindström
José Bonet
Affiliation:
Departamento de Matemática Aplicada E. T. S. Arquitectura Universidad Politécnica de Valencia E-46071 Valencia Spain
Paweł Dománski
Affiliation:
Department of Mathematics Åbo Akademi University FIN-20500 Åbo Finland
Mikael Lindström
Affiliation:
Faculty of Mathematics and Computer Science A. Mickiewicz University Ul. Matejki 48/49 60-769 Poznán Poland
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Abstract

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Every weakly compact composition operator between weighted Banach spaces $H_{v}^{\infty }$ of analytic functions with weighted sup-norms is compact. Lower and upper estimates of the essential norm of continuous composition operators are obtained. The norms of the point evaluation functionals on the Banach space $H_{v}^{\infty }$ are also estimated, thus permitting to get new characterizations of compact composition operators between these spaces.

Keywords

47B3830D5546E15weighted Banach spaces of holomorphic functionscomposition operatorcompact operatorweakly compact operator
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 42 , Issue 2 , 01 June 1999 , pp. 139 - 148
Copyright
Copyright © Canadian Mathematical Society 1999

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