Abstract
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.
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Acknowledgements
This work is supported by the National Natural Science Foundation of China (Nos. 11901323, 11961052, 11761052), the Natural Science Foundation of Inner Mongolia (No. 2018BS01001), the Research Program of Sciences at Universities of Inner Mongolia Autonomous Region (Nos. NJZZ18018, NJZZ20014).
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Communicated by Mostafa Mbekhta.
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Wu, X., Huang, J. Essential spectrum of upper triangular operator matrices. Ann. Funct. Anal. 11, 780–798 (2020). https://doi.org/10.1007/s43034-020-00054-0
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DOI: https://doi.org/10.1007/s43034-020-00054-0