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Essential norms of composition operators and Aleksandrov measures
1997
Pacific Journal of Mathematics
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The essential norm of a composition operator on H 2 is calculated in terms of the Aleksandrov measures of the inducing holomorphic map. The argument provides a purely functiontheoretic 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.
doi:10.2140/pjm.1997.179.59
fatcat:nccw5fhqxzamtma5fbw4bzur2a