Inversion of nonsmooth maps between Banach spaces

Abstract

We study the invertibility nonsmooth maps between infinite-dimensional Banach spaces. To this end, we introduce an analogue of the notion of pseudo-Jacobian matrix of Jeyakumar and Luc in this infinite-dimensional setting. Using this, we obtain several inversion results. In particular, we give a version of the classical Hadamard integral condition for global invertibility in this context.