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The domain space of an analytic composition operator

Published online by Cambridge University Press:  09 April 2009

Thomas Domenig
Affiliation:
Institut für Mathematik, Universität Zürich, Winterthurerstr. 190, CH 8057 Zürich, Switzerland e-mail: [email protected], [email protected], [email protected]
Hans Jarchow
Affiliation:
Institut für Mathematik, Universität Zürich, Winterthurerstr. 190, CH 8057 Zürich, Switzerland e-mail: [email protected], [email protected], [email protected]
Reinhard Riedl
Affiliation:
Institut für Mathematik, Universität Zürich, Winterthurerstr. 190, CH 8057 Zürich, Switzerland e-mail: [email protected], [email protected], [email protected]
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Abstract

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In this paper we show that, for analytic composition operators between weighted Bergman spaces (including Hardy spaces) and as far as boundedness, compactness, order boundedness and certain summing properties of the adjoint are concerned, it is possible to modify domain spaces in a systematic fashion: there is a space of analytic functions which embeds continuously into each of the spaces under consideration and on which the above properties of the operator are decided.

A remarkable consequence is that, in the setting of composition operators between weighted Bergman spaces, the properties in question can be identified as properties of the operator as a map between appropriately chosen Hilbert spaces.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1999

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