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	Semi-fredholm spectrum and Weyl's theorem for operator matrices
	Cao, XH ; Guo, MZ ; Meng, B
	2006
关键词	semi-Fredholm operator Fredholm operator spectrum Weyl&apos s theorem
英文摘要	When A is an element of B( H) and B is an element of B( K) are given, we denote by M(C) an operator acting on the Hilbert space H circle plus K of the form M(C) = (A)(0) (C)(B). In this paper, first we give the necessary and sufficient condition for M(C) to be an upper semi-Fredholm ( lower semi-Fredholm, or Fredholm) operator for some C is an element of B( K, H). In addition, let sigma(SF+)(A) = {lambda is an element of C : A - lambda I is not an upper semi-Fredholm operator} be the upper semi-Fredholm spectrum of A is an element of B( H) and let sigma(SF-)(A) = {lambda is an element of C : A - lambda I is not a lower semi-Fredholm operator} be the lower semi-Fredholm spectrum of A. We show that the passage from sigma(SF +/-)(A) boolean OR sigma(SF +/-)(B) to sigma(SF +/-)(M(C)) is accomplished by removing certain open subsets of sigma(SF-)(A) boolean AND sigma(SF+)(B) from the former, that is, there is an equality sigma(SF +/-)(A) boolean OR sigma(SF +/-)(B) = sigma(SF +/-)(M(C)) boolean OR G, where G is the union of certain of the holes in sigma(SF +/-)(M(C)) which happen to be subsets of sigma(SF-)(A) boolean AND sigma(SF+)(B). Weyl's theorem and Browder's theorem are liable to fail for 2 x 2 operator matrices. In this paper, we also explore how Weyl's theorem, Browder's theorem, a-Weyl's theorem and a-Browder's theorem survive for 2 x 2 upper triangular operator matrices on the Hilbert space.; Mathematics, Applied; Mathematics; SCI(E); 中国科技核心期刊(ISTIC); 中国科学引文数据库(CSCD); 15; ARTICLE; 1; 169-178; 22
语种	英语
出处	SCI
出版者	acta mathematica sinica english series
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/398813]
专题	数学科学学院
推荐引用方式 GB/T 7714	Cao, XH,Guo, MZ,Meng, B. Semi-fredholm spectrum and Weyl's theorem for operator matrices. 2006-01-01.

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