JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (2): 120-126.doi: 10.6040/j.issn.1671-9352.0.2022.487

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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

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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

CLC Number: 

  • O177.2
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