This is an announcement for the paper “Inversion of nonsmooth maps between Banach spaces” by Jesús A. Jaramillohttps://arxiv.org/find/math/1/au:+Jaramillo_J/0/1/0/all/0/1, Sebastián Lajarahttps://arxiv.org/find/math/1/au:+Lajara_S/0/1/0/all/0/1, Óscar Madiedohttps://arxiv.org/find/math/1/au:+Madiedo_O/0/1/0/all/0/1.

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.

The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1712.00565