| Issue |
Wuhan Univ. J. Nat. Sci.
Volume 29, Number 6, December 2024
|
|
|---|---|---|
| Page(s) | 499 - 507 | |
| DOI | https://doi.org/10.1051/wujns/2024296499 | |
| Published online | 07 January 2025 | |
Mathematics
CLC number: O177.2
Property (ω) and Hypercyclic Property for Operators
(ω)性质与算子的亚循环性
1 School of Mathematics and Statistics, Weinan Normal University, Weinan 714099, Shaanxi, China
2 School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710062, Shaanxi, China
Received:
26
February
2024
By means of the new spectrum defined with respect to the property of Consistence in Fredholm and Index (CFI) around an operator, we establish the necessary and sufficient conditions for a bounded linear opeator 
defined on a Hilbert space satisfying the property 
or hypercyclic property. Moreover, the relation between the operators which satisfy the property 
and hypercyclic (supercyclic) property is discussed.
摘要
根据算子周围的一致Fredholm指标性质定义新的谱集， 利用该谱集刻画了Hilbert空间上有界线性算子的
性质或亚循环性质。此外， 研究了满足
性质的算子类和具有亚(超)循环性质的算子类之间的关系。
Key words: property (ω) / consistence in Fredholm and index / hypercyclic operators / supercycilc operators
关键字 : (ω)性质 / 一致Fredholm指标性质 / 亚循环算子 / 超循环算子
Cite this article: DAI Lei, YI Jialu. Property (ω) and Hypercyclic Property for Operators[J]. Wuhan Univ J of Nat Sci, 2024, 29(6): 499-507.
Biography: DAI Lei, male, Ph.D., Professor, research direction: operator theory. E-mail: leidai@yeah.net
Foundation item: Supported by the National Natural Science Foundation of China (11501419) and the Natural Science Basic Research Plan in Shaanxi Province of China(2021JM-519)
© Wuhan University 2024
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