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Weighted composition operators with closed range

Published online by Cambridge University Press:  17 April 2009

N. Palmberg
N. Palmberg
Affiliation:
Department of Mathematics, Åbo Akademi University, Fänriksgatan 3 B, FIN-20500 Åbo, Finland, e-mail: [email protected]
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We study the closed range property of weighted composition operators on weighted Bergman spaces of infinite order (including the Hardy space of infinite order). We give some necessary and sufficient conditions and find a complete characterisation for weighted composition operators associated with conformal mappings. We also give the corresponding results for composition operators on the Bloch-type spaces. Therefore, the results obtained in this paper also improve and generalise the results of Ghatage, Yan, Zheng and Zorboska.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 75 , Issue 3 , June 2007 , pp. 331 - 354
Copyright
Copyright © Australian Mathematical Society 2007

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