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

中文翻译：

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上三角算子矩阵的外尔谱

本文涉及具有给定对角线项的一般 n × n 上三角算子矩阵。基于空间分解技术，给出了其左（右）外尔谱和外尔谱扰动的表征。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）Weyl谱和Weyl谱分别与左（右）Weyl谱和Weyl谱的并集重合。它的对角线条目。