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《山东大学学报(理学版)》 ›› 2024, Vol. 59 ›› Issue (2): 120-126.doi: 10.6040/j.issn.1671-9352.0.2022.487

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局部交换子及其酉系统中的r-重游荡算子

郑宇洁(),刘爱芳*()   

  1. 太原理工大学数学学院, 山西 晋中 030600
  • 收稿日期:2022-09-16 出版日期:2024-02-20 发布日期:2024-02-20
  • 通讯作者: 刘爱芳 E-mail:2751702913@qq.com;liuaifang@tyut.edu.cn
  • 作者简介:郑宇洁(1996—), 女, 硕士研究生, 研究方向为算子理论. E-mail: 2751702913@qq.com
  • 基金资助:
    国家自然科学基金资助项目(11801397)

Local commutant and wandering r-tuple of operators for unitary systems

Yujie ZHENG(),Aifang LIU*()   

  1. College of Mathematics, Taiyuan University of Technology, Jinzhong 030600, Shanxi, China
  • Received:2022-09-16 Online:2024-02-20 Published:2024-02-20
  • Contact: Aifang LIU E-mail:2751702913@qq.com;liuaifang@tyut.edu.cn

摘要:

根据完全游荡向量的相关理论, 引入酉系统中的r-重完全游荡算子以及局部交换子的概念。并给出局部交换子的若干性质。同时, 借助局部交换子得到酉系统的全体r-重完全游荡算子的一个刻画及其他代数性质。最后, 举例说明了主要结果。

关键词: r-重完全游荡算子, 酉系统, 局部交换子, g-标准正交基

Abstract:

According to the theory of completely wandering vector, the concepts of complete wandering operators with multiplicity r for unitary systems and local commutant are introduced. Then the properties of local commutant are given. Meanwhile, a characterization and other algebraic properties of the set of r-tuple complete wandering operators for unitary systems are obtained by means of the local commutators. Finally, some examples are given to illustrate the main results.

Key words: r-tuple complete wandering operator, unitary system, local commutant, g-orthonormal basis

中图分类号: 

  • O177.2
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