标题： 有限幂等自同态的核心偏序关系 显示英文标题

标题： Core partial order for finite potent endomorphisms

摘要： 本文的目的在于利用有限幂零态射将Core逆推广到一般的向量空间。作为应用，在有限幂零态射（指标小于等于一）的集合中研究了Core偏序，从而将该偏序理论推广到无限维向量空间。此外，利用有限幂零态射的CN-分解引入了一个预偏序，并且提出了关于此预偏序的一些问题。在文中还讨论了一些关于任意Hilbert空间中的有界有限幂零态射的评注。 显示英文摘要

摘要： The aim of this paper is to generalize the Core Inverse to arbitrary vector spaces using finite potent endomorphisms. As an application, the core partial order is studied in the set of finite potent endomorphisms (of index lesser or equal than one), thus generalizing the theory of this order to infinite dimensional vector spaces. Moreover, a pre-order is presented using the CN-decomposition of a finite potent endomorphism. Finally, some questions concerning this pre-order are posed. Throughout the paper, some remarks are also made in the framework of arbitrary Hilbert spaces using bounded finite potent endomorphisms.