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Weakly compact composition operators between algebras of bounded analytic functions

Authors: Pablo Galindo, Mikael Lindström and Ray Ryan
Journal: Proc. Amer. Math. Soc. 128 (2000), 149-155
MSC (1991): Primary 46J15; Secondary 46E15, 46G20
Published electronically: May 27, 1999
MathSciNet review: 1646307
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Abstract: We prove a characterization (up to the approximation property) of weakly compact composition operators $C_{\phi }:H^{\infty }(B_{F}) \to H^{\infty }(B_{E})$ in terms of their inducing analytic maps $\phi :B_{E} \to B_{F}$.

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Additional Information

Pablo Galindo
Affiliation: Departamento de Análisis Matemático, Universidad de Valencia, 46100 Burjasot, Valencia, Spain

Mikael Lindström
Affiliation: Department of Mathematics, Åbo Akademi University, FIN-20500 Åbo, Finland

Ray Ryan
Affiliation: Department of Mathematics, University College Galway, Galway, Ireland

Keywords: Weakly compact operator, composition operator, bounded analytic functions on the open unit ball
Received by editor(s): March 10, 1998
Published electronically: May 27, 1999
Additional Notes: Research of the first author was partially supported by DGICYT(Spain) pr. 91-0326.
Communicated by: Steven R. Bell
Article copyright: © Copyright 1999 American Mathematical Society