Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (3): 431-440.

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Essential and Weyl Spectra of 2×2 Bounded Block Operator Matrices

Lin Li1,2(), Alatancang3,*()   

  1. 1 School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021
    2 Department of Mathematics and Computer, Hetao College, Inner Mongolia Bayannur 015000
    3 Department of Mathematics, Hohhot Minzu College, Hohhot 010051
  • Received:2018-06-07 Online:2019-06-26 Published:2019-06-27
  • Contact: Alatancang;
  • Supported by:
    the NSFC(11761029);the NSFC(11861048);the Natural Science Foundation of Inner Mongolia(2016MS0105);the Natural Science Foundation of Hetao College(HYZY201702)


This paper is concerned with the necessary and sufficient conditions that a class of bounded 2×2 block operator matrices are Fredholm operators or Weyl operators. Some necessary and sufficient conditions are given under which the essential spectrum and the Weyl spectrum of the block operator matrix coincide with the essential spectrum and the Weyl spectrum of its entries.

Key words: Essential spectrum, Weyl spectrum, Block operator matrices

CLC Number: 

  • O177.1