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The domain space of an analytic composition operator


Domenig, Thomas; Jarchow, Hans; Riedl, Reinhard (1999). The domain space of an analytic composition operator. Journal of the Australian Mathematical Society, 66(1):56-65.

Abstract

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

Abstract

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

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:National licences > 142-005
Dewey Decimal Classification:Unspecified
Language:English
Date:1 February 1999
Deposited On:01 Nov 2018 16:59
Last Modified:24 Sep 2019 23:41
Publisher:Cambridge University Press
ISSN:1446-7887
OA Status:Green
Publisher DOI:https://doi.org/10.1017/s1446788700036272
Related URLs:https://www.swissbib.ch/Search/Results?lookfor=nationallicencecambridge101017S1446788700036272 (Library Catalogue)

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