摘要
进一步讨论了Fredholm算子的一个重要性质.Fredholm算子是泛函分析算子理论中的一个基本且重要的概念,在偏微分方程等学科方面有重要的应用,在对空间的分类和维数的研究中起着关键的作用.利用现代广义逆扰动稳定的知识给出了一个Fredholm算子在小扰动情形下零空间的维数不变性的一个充分必要条件,即任一个Fredholm算子T0∈F(X,Y),存在充分小的T∈B(X,Y),当且仅当R(T0+T)∩N(T0+)={0}时dimN(T0+T)=dimN(T0).其中T0+是T0的广义逆.
An important characteristic of Fredholm operator is discussed in this paper. As an important fundamental concept in generalized functional and analytical operator theory, Fredholm operator has been used in differential coefficient equations and other fields. It is of vital importance for the research of space classification and dimensions. In 1971, Martin S. gave a result as follows. If T_0∈F(X,Y), then there is an η>0 sufficient small such that T_0+T∈F(X,Y) and dim N(T_0+T)≤dim N(T_0) for any T∈B(X,Y) satisfying ‖T‖<η where F(X,Y) is all of Fredholm operators from X to Y, B(X,Y) denotes all of bounded linear operators from Banach space X to Y, dim N(·) denotes the null-spaceof the operator in the parenthesis.It is shown in this paper that with the same assumptions,dim N(T_0+T)=dim N(T_0) if and only if R(T_0+T)∩N(T_0^+)=｛0｝.
出处
《淮海工学院学报（自然科学版）》
CAS
2004年第4期1-3,共3页
Journal of Huaihai Institute of Technology:Natural Sciences Edition
基金
国家自然科学基金资助项目(10271053)
