We present an infinite-dimensional version of Cartan's theorem concerning the existence of a holomorphic inverse of a given holomorphic self-map of a bounded convex open subset of a dual Banach space. No separability is assumed, contrary to previous analogous results. The main assumption is that the derivative operator is power bounded, and which we, in turn, show to be diagonalizable in some cases, like the separable Hilbert space.

中文翻译：

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Banach 空间上的双全纯映射

我们提出了 Cartan 定理的无限维版本，该定理涉及对偶 Banach 空间的有界凸开子集的给定全纯自映射的全纯逆的存在。与先前的类似结果相反，假定没有可分离性。主要假设是导数算子是幂有界的，并且我们反过来证明它在某些情况下是可对角化的，例如可分离的希尔伯特空间。