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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Item Type: Journal Article, refereed, original work National licences > 142-005 Unspecified English 1 February 1999 01 Nov 2018 16:59 04 Nov 2018 16:17 Cambridge University Press 1446-7887 Green https://doi.org/10.1017/s1446788700036272 https://www.swissbib.ch/Search/Results?lookfor=nationallicencecambridge101017S1446788700036272 (Library Catalogue)

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