Acta mathematica scientia,Series A ›› 2005, Vol. 25 ›› Issue (5): 637-642.

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Perturbation Theorems for Linear Operators

 CAO Xiao-Gong, GUO Mao-Zheng, MENG Bin   

  • Online:2005-10-25 Published:2005-10-25

Abstract:

In this paper, the authors use two subspaces which are introduced by Mbekhta M in 1987 to study the perturbation of linear operators on a Banach space X.  The main result is: suppose that X=K(T)+W, K(T) and W are all closed,dim[K(T)∩N(T)]<∞.If TWW, TW is closed, and there exists a closed subspace N in X such that W=[W∩N(T)]N, and if S∈B(X) is invertible, ST=TS, SWW, and S has sufficiently small norm, then T-S is an upper semi Fredholm operator. If in addition K(T′) is closed and dim N< ∞, then T-S is a Fredholm operator.

Key words: Semi Fredholm operator;Spectrum;Fredholm operator

CLC Number: 

  • 47A10
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