Essential norms of composition operators and Aleksandrov measures
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.
scientific article; zbMATH DE number 950185