关键词: 半Fredholm算子, 谱, Fredholm算子

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