Inversion of nonsmooth maps between Banach spaces

TL;DR

This paper extends the theory of invertibility to nonsmooth maps between infinite-dimensional Banach spaces by introducing an analogue of the pseudo-Jacobian and establishing new inversion criteria, including a Hadamard-type condition.

Contribution

It introduces an infinite-dimensional pseudo-Jacobian concept and derives new inversion results, including a global invertibility criterion akin to Hadamard's condition.

Findings

Established a pseudo-Jacobian analogue for Banach spaces.

Derived a Hadamard-type integral condition for invertibility.

Provided new inversion theorems for nonsmooth maps.

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.