| 有界线性算子的摄动定理 |
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| 引用本文： | 曹小红,郭懋正,孟彬.有界线性算子的摄动定理[J].数学学报,2004,47(2):259-264. |
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| 作者姓名： | 曹小红 郭懋正 孟彬 |
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| 作者单位： | 北京大学数学科学学院应用数学实验室,北京,100871 |
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| 摘 要： | 本文研究了正则算子的摄动理论.考虑Banach空间X上的正则算子T,假设dimK(T)∩N(T)]<∞且K(T)闭,则当S∈B(X)可逆,ST=TS,‖S‖充分小时,证明了T—S为上半Fredholm算子.在以上条件下,若K(T)+N(T)或者R(T)+N(T)在X中有有限维的补子空间,这时T—S为Fredholm算子.
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| 关 键 词： | 正则算子 单值扩张性质 半Fredholm算子 |
| 文章编号： | 0583-1431(2004)02-0259-06 |
Perturbation Theorem for Bounded Linear Operator |
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| Xiao Hong CAO Mao Zheng GUO Bin MEM.Perturbation Theorem for Bounded Linear Operator[J].Acta Mathematica Sinica,2004,47(2):259-264. |
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| Authors: | Xiao Hong CAO Mao Zheng GUO Bin MEM |
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| Institution: | Xiao Hong CAO Mao Zheng GUO Bin MEM (LMAM, Department of Mathematics, Peking University, Beijing 100871, P. R. China) |
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| Abstract: | If T is a regular operator on a Banach space X, with finite dimensional intersection K(T) ∩ N(T) and K(T) closed, and if 5 is invertible, commutes with T and has sufficiently small norm, then T - S is an upper semi-Fredholm operator. If in addition K(T) + N(T) or R(T) + N(T) has a complementary subspace with finite dimension, then T ?S is a Fredholm operator. |
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| Keywords: | Regular operator Single-valued extension property Semi-Fredholm operator |
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