Characterizations for the Core Invertibility and EP-ness Involving Projections.

In this paper we obtain some equivalent conditions for the core invertibility and EP-ness of 1 − p q , 1 − p q p , p − p q and p − q , where p , q are projections in different settings, such as ∗-rings, ∗-reducing rings and C ∗ -algebras. Moreover, several representations for the core inverses of product, difference and sum of two generalized projections are derived. In particular, a number of examples are given to illustrate our results. [ABSTRACT FROM AUTHOR]