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.

中文翻译：

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Banach空间之间非光滑贴图的反演

我们研究了无限维Banach空间之间的可逆非光滑映射。为此，我们在此无穷维设置中引入了Jeyakumar和Luc的伪Jacobi矩阵概念的类似物。使用此方法，我们获得了几个反演结果。特别是，在这种情况下，我们给出了经典Hadamard积分条件的一个版本，用于全局可逆性。