论文标题
巴拉赫空间上的扰动操作员
Perturbed Operators on Banach Spaces
论文作者
论文摘要
令x为k = r或c上的banach空间，让f：= f+c成为从x到x的弱强制算子，其中f是c^1-operator，而C c a c^1紧凑型操作员。提供了足够的条件，以断言扰动的操作员F是C^1-diffeomormorlism。给出了三个推论。第一个，当F是线性同构时。第二个，当f是身份的k缩合性扰动时。第三个，当x是希尔伯特空间，而特定的线性操作员。我们结果的证明是基于弗雷德尔姆操作员的属性，以及本地和全局的倒数映射定理以及Banach固定点定理。作为应用程序，给出了两个示例
Let X be a Banach Space over K=R or C, and let f:=F+C be a weakly coercive operator from X onto X, where F is a C^1-operator, and C a C^1 compact operator. Sufficient conditions are provided to assert that the perturbed operator f is a C^1-diffeomorphism. Three corollaries are given. The first one, when F is a linear homeomorphism. The second one, when F is a k-contractive perturbation of the identity. The third one, when X is a Hilbert space and F a particular linear operator. The proof of our results is based on properties of Fredholm operators, as well as on local and global inverse mapping theorems, and the Banach fixed point theorem. As an application two examples are given
