Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (6): 1611-1618.

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The Essential Spectrum of a Class of Anti-Triangular Operator Matrices

Rui Hua,Yaru Qi*()   

  1. College of Sciences, Inner Mongolia University of Technology, Hohhot 010051
  • Received:2022-02-09 Online:2022-12-26 Published:2022-12-16
  • Contact: Yaru Qi
  • Supported by:
    the Natural Science Foundation of China(12261065);the National Natural Science Foundation of Inner Mongolia(2021LHMS01004);the National Natural Science Foundation of Inner Mongolia(2022MS01005);the Basic Science Research Fund in the Universities Directly under the Inner Mongolia Autonomus Region(JY20220151)


In this paper, the essential spectrum of a class of unbounded unself-adjoint anti-triangular operator matrices is studied. Firstly, we describe the essential spectrum of operator matrices by using the quadratic operator pencil and the properties of its operator entries, and estimate the essential spectrum of the whole operator matrix. On this basis, the accumulation point of the non-real spectrum of the operator matrix is analyzed.

Key words: Anti-triangular operator matrices, Essential spectrum, Accumulation points of spectrum

CLC Number: 

  • O177.1