The aim of this work is to develop a general theory of core-nilpotent endomorphisms of arbitrary vector spaces, such that endomorphisms of finite-dimensional vector spaces and finite potent endomorphisms of infinite-dimensional vector spaces are particular cases of the CN-endomorphisms studied in this theory. For these CN-endomorphisms, we introduce an index that generalizes the index of a finite square matrix and we prove the existence of the Drazin inverse and reflexive generalized inverses. In particular, we characterize all endomorphisms that have Drazin inverse on arbitrary vector spaces. Moreover, we offer a method to study infinite linear systems associated with CN-endomorphisms.

这项工作的目的是发展一个任意向量空间的核心-幂等内同态的一般理论，从而使有限维向量空间的内同态和无限维向量空间的有限有效内同构成为CN-内同态的特殊情况。这个理论。对于这些CN同态，我们引入了一个索引，将广义方阵的索引广义化，并证明了Drazin逆和自反广义逆的存在。特别是，我们表征了在任意向量空间上具有Drazin逆的所有同态。此外，我们提供了一种研究与CN内同态有关的无限线性系统的方法。