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On the Compactness of the Composition Operator | ||
| journal of al-qadisiyah for pure science(quarterly) | ||
| Article 1, Volume 13, Issue 3, 2013, Pages 32-39 PDF (0 K) | ||
| Author | ||
| Aqeel Mohammed Hussein | ||
| Abstract | ||
| Let U denote the unit ball in the complex plane, the Hardy space is the set of functions holomorphic on U such that with denotes then the Taylor coefficient of f . Let be a holomorphic self-map of U, the composition operator induced by is defined on by the equation In this paper we have studied the compactness of the composition operator induced by the bijective map and discussed the adjoint the compactness of the composition operator of the map .We give some theorems on compactness of the composition operators. We have look also at some known properties on composition operators and tried to see the analogue properties in order to show how the results are changed by changing the map in U. In order to make the work accessible to the reader, we have included some known results with the details of the proofs for some cases and proofs for the properties . | ||
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