Generalized regular points of a C^1 map between Banach spaces  

Banach空间之间C^1映射的广义正则点(英文)

作　　者：史平[1] 马吉溥[2] 

机构地区：[1]南京财经大学应用数学系,南京210003 [2]南京大学数学系,南京210093

出　　处：《Journal of Southeast University(English Edition)》2007年第1期148-150,共3页东南大学学报（英文版）

基　　金：The National Natural Science Foundation of China(No10271053);the Foundation of Nanjing University of Finance andEconomics (NoB0556)

摘　　要：Let f be a C^1 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, iff ＇（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 xo is a generalized regular point off if and only if the multi-index （M（x）, Me（x）, Mr（x）） is continuous at X0.设f是2个Banach空间E和F之间C1映射.已经证明f的广义正则点概念是f的正则点概念的一个推广并且在非线性分析和大范围分析中有非常重要的应用.用f产生的在x0∈E处的3个整数(或无穷大)值指标M(x0),Mc(x0)和Mr(x0)和分析Banach空间上有界线性算子的广义逆来刻画f的广义正则点,即,如果f′(x0)在从E上到F的有界线性算子组成的Banach空间B(E,F)内有广义逆,且M(x0),Mc(x0)和Mr(x0)中至少有一个是有限,则x0是f的广义正则点的充分必要条件是多重指标(M(x),M(x),M(x))在x点处连续.

关 键 词：Banach space bounded linear operator generalized inverse index generalized regular point semi- Fredholm mao 

分 类 号：O177.91[理学—数学]