Property(ω) and Hypercyclic Property for Operators  

(ω)性质与算子的亚循环性

作　　者：DAI Lei YI Jialu 戴磊;伊佳璐(渭南师范学院数学与统计学院,陕西渭南714099;陕西师范大学数学与统计学院,陕西西安710062)

机构地区：[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

出　　处：《Wuhan University Journal of Natural Sciences》2024年第6期499-507,共9页武汉大学学报(自然科学英文版)

基　　金：Supported by the National Natural Science Foundation of China (11501419);the Natural Science Basic Research Plan in Shaanxi Province of China(2021JM-519)。

摘　　要：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 T defined on a Hilbert space satisfying the property(ω)or hypercyclic property.Moreover,the relation between the operators which satisfy the property(ω)and hypercyclic(supercyclic)property is discussed.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(ω)性质或亚循环性质。此外,研究了满足(ω)性质的算子类和具有亚(超)循环性质的算子类之间的关系。

关 键 词：property(ω) consistence in Fredholm and index hypercyclic operators supercycilc operators 

分 类 号：O177.2[理学—数学]