Rank One Perturbation of Unitary Operators with Full Measure of Hypercyclic Vectors
Rank One Perturbation of Unitary Operators with Full Measure of Hypercyclic Vectors
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DOI：
10.1007/s40840-022-01334-9
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发表时间：
2022-06
影响因子：
1.2
通讯作者：
Xin Liu;Zhi-Jing Chen
中科院分区：
文献类型：
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作者：
Xin Liu;Zhi-Jing Chen
在本文中，我们发现一类酉算子，表示为，在复数可分无限维希尔伯特空间上，使得对于任意一个，存在一个秩为1的算子R，这样它是超循环的，并且超循环向量是完全测度的。然后，这些结果应用于离散时间线性控制系统的可控性，其中一级扰动用作一维反馈控制律。
In this note, we find a class of unitary operators, denoted by, on a complex separable infinite-dimensional Hilbert spacesuch that for any, there exists an operatorRof rank 1 onsuch thatis hypercyclic and the hypercyclic vectors are of full measure. Then, these results are applied to the controllability of discrete-time linear control systems, where the rank one perturbation is used as a one-dimensional feedback control law.