东南大学学报（英文版）
東南大學學報（英文版）
동남대학학보（영문판）
JOURNAL OF SOUTHEAST UNIVERSITY
2007年
1期
148-150
,共3页
Banach空间%有界线性算子%广义逆%指标%广义正则点%半Fredholm映射
Banach空間%有界線性算子%廣義逆%指標%廣義正則點%半Fredholm映射
Banach공간%유계선성산자%엄의역%지표%엄의정칙점%반Fredholm영사
Banach space%bounded linear operator%generalized inverse%index%generalized regular point%semi-Fredholm map
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),Mc(x),Mr(x)) 在x0点处连续.
設f是2箇Banach空間E和F之間C1映射.已經證明f的廣義正則點概唸是f的正則點概唸的一箇推廣併且在非線性分析和大範圍分析中有非常重要的應用.用f產生的在x0∈E處的3箇整數(或無窮大)值指標M(x0),Mc(x0) 和Mr(x0)和分析Banach空間上有界線性算子的廣義逆來刻畫f的廣義正則點,即,如果 f '(x0) 在從E上到F的有界線性算子組成的Banach空間B(E,F)內有廣義逆,且M(x0),Mc(x0) 和Mr(x0) 中至少有一箇是有限,則 x0 是f的廣義正則點的充分必要條件是多重指標(M(x),Mc(x),Mr(x)) 在x0點處連續.
설f시2개Banach공간E화F지간C1영사.이경증명f적엄의정칙점개념시f적정칙점개념적일개추엄병차재비선성분석화대범위분석중유비상중요적응용.용f산생적재x0∈E처적3개정수(혹무궁대)치지표M(x0),Mc(x0) 화Mr(x0)화분석Banach공간상유계선성산자적엄의역래각화f적엄의정칙점,즉,여과 f '(x0) 재종E상도F적유계선성산자조성적Banach공간B(E,F)내유엄의역,차M(x0),Mc(x0) 화Mr(x0) 중지소유일개시유한,칙 x0 시f적엄의정칙점적충분필요조건시다중지표(M(x),Mc(x),Mr(x)) 재x0점처련속.
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.
