QUASI-LOCAL CONJUGACY THEOREMS IN BANACH SPACES  

作　　者：ZHANG WEIRONG MA JIPu 

机构地区：[1]Department of Mathematics, Nanjing University, Nanjing 210093, China.

出　　处：《Chinese Annals of Mathematics,Series B》2005年第4期551-558,共8页数学年刊（B辑英文版）

基　　金：Project supported by the National Natural Science Foundation of China (No. 10271053).

摘　　要：Let f ： U（x0） belong to E → F be a C^1 map and f＇（x0） be the Frechet derivative of f at x0. In local analysis of nonlinear functional analysis, implicit function theorem, inverse function theorem, local surjectivity theorem, local injectivity theorem, and the local conjugacy theorem are well known. Those theorems are established by using the properties： f＇（x0） is double splitting and R（f＇（x）） ∩ N（T0^＋） = {0} near x0. However, in infinite dimensional Banach spaces, f＇（x0） is not always double splitting （i.e., the generalized inverse of f（x0） does not always exist）, but its bounded outer inverse of f＇（x0） always exists. Only using the C^1 map f and the outer inverse To^# of f（x0）, the authors obtain two quasi-local conjugacy theorems, which imply the local conjugacy theorem if x0 is a locally fine point of f. Hence the quasi-local conjugacy theorems generalize the local conjugacy theorem in Banach spaces.

关 键 词：Frechet derivative Quasi-local conjugacy theorems Outer inverse Local conjugacy theorem 

分 类 号：O177.2[理学—数学]