| 张利.Hα∞到Hβ∞复合算子的线性组合*[J].数学年刊A辑,2023,44(2):121~132 |
| Hα∞到Hβ∞复合算子的线性组合* |
| Linear Combinations of Composition Operators from Hα∞ to Hβ∞ |
| Received:September 06, 2022 Revised:March 21, 2023 |
| DOI：10.16205/j.cnki.cama.2023.0010 |
| 中文关键词: 复合算子, 线性组合, 抵消性 |
| 英文关键词:Composition operators, Linear combinations, Cancellation property |
| 基金项目:南阳师范学院自然科学基金 (No.QN2017047) |
|
| Hits: 849 |
| Download times: 1851 |
| 中文摘要: |
| 设B是N维复空间CN中的开单位球, ?i为B上的解析自映射,Hα∞ 表示定义在单位球上的加权解析函数空间. 本文主要研究的是从空间Hα∞到Hβ∞上的复合算子线性组合MPi=1 λiC?i 的紧致性, 其中 λi(i = 1, 2, · · · , M) 是非零常数.另外, 根据紧致性等价条件, 得出算子差分对(C?1 - C?2)-(C?3 - C?1)是紧致的当且仅当C?1 - C?2与C?3 - C?1都是紧致的算子. |
| 英文摘要: |
| For i = 1, 2, · · · , M, let λi be nonzero numbers, B be the unit ball of the complex space CN , ?i be self-maps of B, and Hα∞ be the weighted holomorphic function space on B. The compactness of linear combinations of composition operators MPi=1 λiC?i from Hα∞ to Hβ∞ is discussed in this paper. Moreover, using an equivalent condition of compactness, the author shows that the double difference cancellation (C?1 - C?2 ) ? (C?3 - C?1 ) is compact if and only if both C?1 - C?2 and C?3 - C?1 are compact. |
| View Full Text View/Add Comment Download reader |
| Close |
|
|
|
|
|
