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Essential norms of
composition operators and Aleksandrov measures
Joseph A. Cima and Alec L. Matheson |
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Vol. 179 (1997), No. 1, 59–64
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Abstract |
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The essential norm of a composition operator on H2 is calculated in terms 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 L1 and Shapiro’s compactness condition for composition operators on Hardy spaces. An application is given relating the essential norm to angular derivatives. |
Milestones
Received: 6 September 1995
Revised: 29 March 1996
Published: 1 May 1997
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Authors |
| Joseph A. Cima | |
| University of North Carolina Chapel Hill, NC |
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| Alec L. Matheson | |
| Lamar University Beaumont, TX 77710 |
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