$2\times 2$ 上三角分块算子矩阵的 Jeribi 本质谱

Abstract

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.

CLC Number:

O175.3

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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References 12

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

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