Essential norms of composition operators and Aleksandrov measures
type: Item
instance of: scholarly article
title: Essential norms of composition operators and Aleksandrov measures
zbMATH Open document ID: 0871.47027
author: Joseph A. Cima
author: Alec L. Matheson
published in: Pacific Journal of Mathematics
publication date: 1997-09-09T00:00:00Z
full work available at URL: v179no1.html
review text: 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.
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 30D55
zbMATH DE Number: 950185
zbMATH Keywords: essential norm
zbMATH Keywords: composition operator
zbMATH Keywords: Aleksandrov measures
zbMATH Keywords: angular derivatives
MaRDI profile type: Publication
OpenAlex ID: W2129129954
DOI: 10.2140/PJM.1997.179.59
description: scientific article; zbMATH DE number 950185