数学物理学报 ›› 2005, Vol. 25 ›› Issue (5): 637-642.
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曹小红, 郭懋正, 孟彬
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CAO Xiao-Gong, GUO Mao-Zheng, MENG Bin
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摘要：
该文利用Mbekhta M于1987年引入的两个子空间来研究线性算子的摄动. 证明了如下结论：设X=K(T)+W, 其中K(T), W均闭, dim［K(T)∩N(T)］< ∞. 若TWW, TW闭, 且存在闭子空间N, 使W=［W∩N(T)］N, 则： 当S∈B(X)可逆, ST= TS, SWW, 且‖S‖充分小时， T-S为上半Fredholm算子. 在上条件下, 若dimN<∞, K(T′)闭, 则T-S为Fredholm算子, 且R(T-S)=X.
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 TWW, 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, SWW, 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
中图分类号:
曹小红, 郭懋正, 孟彬. 线性算子的摄动定理[J]. 数学物理学报, 2005, 25(5): 637-642.
CAO Xiao-Gong, GUO Mao-Zheng, MENG Bin. Perturbation Theorems for Linear Operators[J]. Acta mathematica scientia,Series A, 2005, 25(5): 637-642.
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http://121.43.60.238/sxwlxbA/CN/Y2005/V25/I5/637
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