Compact Differences of Composition Operators over Polydisks
Compact Differences of Composition Operators over Polydisks
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DOI：
10.1007/s00020-012-1962-z
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发表时间：
2012-03
影响因子：
0.8
通讯作者：
B. Choe;H. Koo;Inyoung Park
中科院分区：
文献类型：
--
作者：
B. Choe;H. Koo;Inyoung Park
Moorhouse刻画了复平面单位圆盘上加权Bergman空间上复合算子的紧差。她还发现了一个充分条件，一个单一的组成运营商是一个紧凑的扰动的总和给予considermany组成运营商和研究的作用，二阶数据在确定紧凑的差异。本文在Stessin和Zhu关于加权Bergman空间上的复合算子的有界性和紧性的刻画的基础上，通过在主要步骤上的不同处理，得到了Moorhouse结果的多圆盘类似.此外，我们找到了一个必要的系数关系，紧凑的组合，这是第一次注意到磁盘上的Kriete和Moorhouse。
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.