Pseudo core invertibility in rings and its applications

We present new additive results regarding the pseudo core inverse in a ring with involution. We establish the necessary and sufficient conditions under which the sum of two pseudo core invertible elements in a ring is also pseudo core invertible. As an application, we investigate the pseudo core invertibility of operator matrices. These findings extend the additive result on pseudo core invertibility by Gao and Chen [Comm. Algebra, 46 (2018), 38-50].