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Essential spectrum of upper triangular operator matrices
Annals of Functional Analysis ( IF 1 ) Pub Date : 2020-02-05 , DOI: 10.1007/s43034-020-00054-0
Xiufeng Wu , Junjie Huang

This paper is concerned with general $$n\times n$$ upper-triangular operator matrices with given diagonal entries. The characterizations of perturbations of their left (right) essential spectrum and essential spectrum are given, based on the space decomposition technique. Moreover, some sufficient and necessary conditions are given under which the left (right) essential spectrum and the essential spectrum of such operator matrix, respectively, coincide with the union of the left (right) essential spectrum and the essential spectrum of its diagonal entries.

中文翻译:

上三角算子矩阵的基本谱

本文涉及具有给定对角线项的一般 $$n\times n$$ 上三角算子矩阵。基于空间分解技术,给出了它们的左(右)基本谱和基本谱的扰动特征。此外,给出了一些充分必要条件,在这些条件下,该算子矩阵的左(右)本征谱和本征谱分别与左(右)本征谱及其对角线项的本征谱的并集重合。
更新日期:2020-02-05
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