We define and characterize the core inverse in the context of Banach algebras. The Banach space operator case is also considered. Using the core inverse, we present new characterizations of EP Banach space operators and EP Banach algebra elements. The dual core inverse for Banach algebra elements is presented too. Some new characterizations of co–EP Banach algebra elements are given by means the core inverse and dual core inverse.

中文翻译：

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Banach 代数中的核心逆

我们在 Banach 代数的上下文中定义和表征核心逆。还考虑了 Banach 空间算子的情况。使用核心逆，我们提出了 EP Banach 空间算子和 EP Banach 代数元素的新特征。也给出了 Banach 代数元素的双核逆。co-EP Banach 代数元素的一些新特征通过核逆和双核逆给出。