Perturbed Operators on Banach Spaces
Functional Analysis
2020-07-10 v1
Abstract
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
Cite
@article{arxiv.2007.04665,
title = {Perturbed Operators on Banach Spaces},
author = {José María Soriano Arbizu and Manuel Odóñez Cabrera},
journal= {arXiv preprint arXiv:2007.04665},
year = {2020}
}
Comments
15 pages