Essential norms of composition operators and Aleksandrov measures (Q1816511)
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scientific article; zbMATH DE number 950185
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Essential norms of composition operators and Aleksandrov measures |
scientific article; zbMATH DE number 950185 |
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Essential norms of composition operators and Aleksandrov measures (English)
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9 September 1997
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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.
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essential norm
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composition operator
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Aleksandrov measures
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angular derivatives
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