一类反三角算子矩阵的本质谱

数学物理学报 ›› 2022, Vol. 42 ›› Issue (6): 1611-1618.

一类反三角算子矩阵的本质谱

花蕊,齐雅茹*()

^{内蒙古工业大学理学院, 呼和浩特 010051}

收稿日期:2022-02-09 出版日期:2022-12-26 发布日期:2022-12-16
通讯作者: 齐雅茹 E-mail:qiyaru@imut.edu.cn
基金资助:
国家自然科学基金(12261065);内蒙古自然科学基金(2021LHMS01004);内蒙古自然科学基金(2022MS01005);自治区直属高校基本科研业务费项目(JY20220151)

The Essential Spectrum of a Class of Anti-Triangular Operator Matrices

Rui Hua,Yaru Qi*()

^{College of Sciences, Inner Mongolia University of Technology, Hohhot 010051}

Received:2022-02-09 Online:2022-12-26 Published:2022-12-16
Contact: Yaru Qi E-mail:qiyaru@imut.edu.cn
Supported by:
the Natural Science Foundation of China(12261065);the National Natural Science Foundation of Inner Mongolia(2021LHMS01004);the National Natural Science Foundation of Inner Mongolia(2022MS01005);the Basic Science Research Fund in the Universities Directly under the Inner Mongolia Autonomus Region(JY20220151)

摘要/Abstract

摘要：

该文讨论了一类无界非自伴反三角算子矩阵的本质谱.利用二次算子族及其矩阵内部元素的性质等价刻画了算子矩阵的本质谱, 并在此基础上估计了算子矩阵的本质谱的范围.最后基于本质谱的研究, 讨论了其非实谱的聚点问题.

关键词: 反三角算子矩阵, 本质谱, 谱的聚点

Abstract:

In this paper, the essential spectrum of a class of unbounded unself-adjoint anti-triangular operator matrices is studied. Firstly, we describe the essential spectrum of operator matrices by using the quadratic operator pencil and the properties of its operator entries, and estimate the essential spectrum of the whole operator matrix. On this basis, the accumulation point of the non-real spectrum of the operator matrix is analyzed.

Key words: Anti-triangular operator matrices, Essential spectrum, Accumulation points of spectrum

中图分类号:

O177.1

花蕊,齐雅茹. 一类反三角算子矩阵的本质谱[J]. 数学物理学报, 2022, 42(6): 1611-1618.

Rui Hua,Yaru Qi. The Essential Spectrum of a Class of Anti-Triangular Operator Matrices[J]. Acta mathematica scientia,Series A, 2022, 42(6): 1611-1618.

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