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Weyl Spectrum of Upper Triangular Operator Matrices

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Abstract

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.

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Acknowledgements

We thank the referees for their time and comments.

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Authors and Affiliations

  1. School of Mathematical Sciences, Inner Mongolia Normal University, Hohhot, 010022, P. R. China

    Xiu Feng Wu

  2. School of Mathematical Sciences, Inner Mongolia University, Hohhot, 010021, P. R. China

    Jun Jie Huang

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  1. Xiu Feng Wu
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  2. Jun Jie Huang
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Correspondence to Xiu Feng Wu.

Additional information

Supported by National Natural Science Foundation of China (Grant Nos. 11901323 and 11961052), Natural Science Foundation of Inner Mongolia of China (Grant No. 2018BS01001), the Research Program of Sciences at Universities of Inner Mongolia Autonomous Region (Grant Nos. NJZZ18018) and SPH-IMUN (Grant No. 2017YJRC018)

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Wu, X.F., Huang, J.J. Weyl Spectrum of Upper Triangular Operator Matrices. Acta. Math. Sin.-English Ser. 36, 783–796 (2020). https://doi.org/10.1007/s10114-020-9485-z

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  • DOI: https://doi.org/10.1007/s10114-020-9485-z

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