Cancellation properties of composition operators on Bergman spaces
Cancellation properties of composition operators on Bergman spaces
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Bergman空间上复合算子的消去性质
DOI：
10.1016/j.jmaa.2015.07.027
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发表时间：
2015-12-15
影响因子：
1.3
通讯作者：
Wang, Maofa
中科院分区：
文献类型：
--
作者：
Koo, Hyungwoon;Wang, Maofa
单位圆盘上Bergman空间上两个复合算子的紧致差用[11]表示，其特征是每个“坏”边界点上的诱导映射具有一定的消去性质，这使得单个复合算子不紧致。在Bergman空间中，我们完整地刻画了三个复合算子的线性组合的紧性。作为这个表征的一个结果，我们证明复合算子的双差分的紧性没有消去性质。更准确地说，我们证明如果(i)是不同的并且c - i都不是紧致的，那么(c - 1 - c - 2) - (c - 3 - c - 1)是紧致的当且仅当（c - 1 - c - 2）和（c - 3 - c - 1）都是紧致的。(C) 2015爱思唯尔公司版权所有。
The compact difference of two composition operators on the Bergman spaces over the unit disc is characterized in [11] in terms of certain cancellation property of the inducing maps at every "bad" boundary points, which make each single composition operator not to be compact. In this paper, we completely characterize the compactness of a linear combination of three composition operators on the Bergman space. As one consequence of this characterization, we show that there is no cancellation property for the compactness of double difference of composition operators. More precisely, we show that if phi(i) are distinct and none of C-phi i is compact, then (C-phi 1 - C-phi 2) - (C-phi 3 - C-phi 1) is compact if and only if both (C-phi 1 - C-phi 2) and (C-phi 3 - C-phi 1) are compact. (C) 2015 Elsevier Inc. All rights reserved.