Local conjugacy theorems for C1 operators between Banach manifolds

Abstract

In this paper, by the generalized inverse theory of bounded linear operators, the local conjugacy theorem for C 1 operators between Banach manifolds is established. According to this theorem, the conditions which can be used to make sure that a C 1 operator can be linearized are provided. Local conjugacy theorems for nonlinear Fredholm operators, nonlinear semi-Fredholm operators and finite rank operators are introduced.