A generalization of the co-EP property. Issue 8 (3rd August 2022) - Zou, Honglin; Cvetković Ilić, Dragana; Zuo, Kezheng
Abstract: We establish different characterizations for the invertibility of ab − ba in a ring when b ∈ a 1, 2 and b ∈ a 1 that are related to the invertibility of elements expressed as certain functions of a, b and suitable elements from the center of the ring. As a consequence we get some interesting results in the matrix and operator settings: for a co-EP matrix (or operator) A we list all linear combinations of A, A †, A A †, A † A, A ( A † ) 2 A, A † A 2 A † that are invertible independently of the choice of the scalars. In addition, we consider the co-EP-ness of idempotents and tripotents.