Compact Differences of Composition Operators over Polydisks |
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Authors: | Email author" target="_blank">Boo?Rim?ChoeEmail author Hyungwoon?Koo Inyoung?Park |
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Institution: | 1.Department of Mathematics,Korea University,Seoul,Korea;2.BK21-Mathematical Sciences Division,Seoul National University,Seoul,Korea |
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Abstract: | Moorhouse characterized compact differences of composition operators acting on a weighted Bergman space over the unit disk
of the complex plane. She also found a sufficient condition for a single composition operator to be a compact perturbation
of the sum of given finitely many composition operators and studied the role of second order data in determining compact differences.
In this paper, based on the characterizations due to Stessin and Zhu, of boundedness and compactness of composition operators
acting from a weighted Bergman space into another, we obtain the polydisk analogues of Moorhouse’s results through a different
approach in main steps. In addition we find a necessary coefficient relation for compact combinations which was first noticed
on the disk by Kriete and Moorhouse. |
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