东南大学学报（英文版）2007，Vol.23Issue(1)：148-150,3.
Banach空间之间C1映射的广义正则点
Generalized regular points of a C1 map between Banach spaces
摘要
Abstract
Let f be a C1 map between two Banach spaces E and F.It has been proved that the concept of generalized regular points of f,which is a generalization of the notion of regular points of f,has some crucial applications in nonlinearity and global analysis.We characterize the generalized regular points of f using the three integer-valued (or infinite) indices M(x0),Mc(x0) and Mr(x0) at x0∈E generated by f and by analyzing generalized inverses of bounded linear operators on Banach spaces,that is,if f '(x0) has a generalized inverse in the Banach space B(E,F) of all bounded linear operators on E into F and at least one of the indices M(x0), Mc(x0) and Mr(x0) is finite,then x0 is a generalized regular point of f if and only if the multi-index (M(x),Mc(x),Mr(x)) is continuous at x0.关键词
Banach空间/有界线性算子/广义逆/指标/广义正则点/半Fredholm映射Key words
Banach space/bounded linear operator/generalized inverse/index/generalized regular point/semi-Fredholm map分类
数理科学引用本文复制引用
史平,马吉溥..Banach空间之间C1映射的广义正则点[J].东南大学学报（英文版）,2007,23(1):148-150,3.基金项目
The National Natural Science Foundation of China (No.10271053),the Foundation of Nanjing University of Finance and Economics (No.B0556). （No.10271053）
