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Pacific Journal of Mathematics
Article . 1997 . Peer-reviewed
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Essential norms of composition operators and Aleksandrov measures

descriptionPublicationkeyboard_double_arrow_right Article 01 May 1997Publisher:Mathematical Sciences PublishersJournal:Pacific Journal of Mathematics, volume 179, pages 59-64 (issn: 0030-8730, Copyright policy )
Authors: Alec Matheson; Joseph A. Cima;

doi: 10.2140/pjm.1997.179.59

Essential norms of composition operators and Aleksandrov measures

Abstract

The essential norm of a composition operator on \(H^2\) is calculated in terms of the singular parts of the Aleksandrov measures of the inducing holomorphic map. The argument provides a purely function-theoretic proof of the equivalence of Sarason's compactness condition for composition operators on \(L^1\) and Shapiro's compactness condition for composition operators on Hardy spaces. An application is given relating the essential norm to angular derivatives.

Keywords

angular derivatives, Linear operators on function spaces (general), essential norm, Aleksandrov measures, composition operator, \(H^p\)-classes

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
32
Top 10%
Top 10%
Average
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