$2\times 2$ 上三角分块算子矩阵的 Jeribi 本质谱

数学物理学报 ›› 2026, Vol. 46 ›› Issue (3): 929-938.

$2\times 2$ 上三角分块算子矩阵的 Jeribi 本质谱

石慧芳, 吴德玉^*()

内蒙古大学数学科学学院呼和浩特 010021

收稿日期:2025-04-08 修回日期:2025-06-27 出版日期:2026-06-26 发布日期:2026-06-16
通讯作者: 吴德玉 E-mail:3355679774@qq.com
基金资助:
国家自然科学基金(12561022);内蒙古自然科学基金(2023MS01019);内蒙古自然科学基金(2022ZD05);呼和浩特民族学院博士项目(MZXYBS202307)

The Jeribi Essential Spectrum of $2\times 2$ Upper Triangular Block Operator Matrices

Huifang Shi, Deyu Wu^*()

School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021

Received:2025-04-08 Revised:2025-06-27 Online:2026-06-26 Published:2026-06-16
Contact: Deyu Wu E-mail:3355679774@qq.com
Supported by:
NSFC(12561022);NSFIM(2023MS01019);NSFIM(2022ZD05);Doctoral Program of Hohhot Minzu College(MZXYBS202307)

摘要/Abstract

摘要：

设 $X$ 是复无穷维 Banach 空间, 该文主要研究 $X\times X$ 上的 $2\times 2$ 上三角分块算子矩阵 $T=\left[\begin{array}{cc}A & B \\0 & D\end{array}\right]$ 的 Jeribi 本质谱. 利用内部元 $A$ 和 $D$ 的 Jeribi 本质谱来刻画算子矩阵 $T$ 的 Jeribi 本质谱. 给出了 $\hat{\sigma_{J}}(T)=\sigma_{J}(A)\cup\sigma_{J}(D)$ 成立的充分条件. 还给出了分块算子矩阵 $T$ 的 Jeribi 本质谱和 $A,D$ 的其他谱的关系.

关键词: Banach 空间, 上三角分块算子矩阵, Jeribi 本质谱, Fredholm 算子.

Abstract:

Let $X$ be a complex infinite dimensional Banach space. In this paper, we mainly study the $2\times 2$ upper triangular block operator matrix $T=\left[\begin{array}{cc}A & B \\0 & D\end{array}\right]$ on $X\times X$. By using the Jeribi essential spectrum of entries $A$ and $D$ to characterize the Jeribi essential spectrum of operator matrix $T$. Some sufficient conditions for the relationship $\hat{\sigma_{J}}(T)=\sigma_{J}(A)\cup\sigma_{J}(D)$ hold are given. Also, the relationship between the Jeribi essential spectrum of operator matrix $T$ and other spectrum of $A,D$ are given.

Key words: Banach space, upper triangular block operator matrix, Jeribi essential spectrum, Fredholm operator.

中图分类号:

O175.3

石慧芳, 吴德玉. $2\times 2$ 上三角分块算子矩阵的 Jeribi 本质谱[J]. 数学物理学报, 2026, 46(3): 929-938.

Huifang Shi, Deyu Wu. The Jeribi Essential Spectrum of $2\times 2$ Upper Triangular Block Operator Matrices[J]. Acta mathematica scientia,Series A, 2026, 46(3): 929-938.

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