The one-sided EP invertibility and the related generalized inverses
Long Wang, Peipei Zhai, Tingting Li, Honglin Zou · Communications in Algebra · 2025
In this article, we firstly investigate some properties of one-sided core inverses. Particularly, new characterizations for left core inverses are given in terms of projections and units. Also, we introduced a new one-side generalized inverse which is called one-sided EP-inverse. Given a∈R, we say that a is left EP-invertible if there exists an x∈R such that axa=a, (ax)∗=ax, xa2=a and x2a=x. Several characterizations of the left EP-invertibility are derived. For instance, it is proved that a is left EP-invertible if and only if there exists an x∈R such that axa=a, (ax)∗=ax and x2a=x. Moreover, it is also proven that a is left EP-invertible if and only if a∈a∗R∩Ra∗a. Finally, we introduce the right EP-invertibility and obtain some results dual to those on the (right) EP-invertibility.