A generalization of the co-EP property. Issue 8 (3rd August 2022)

• Record Type: Journal Article
• Authors: Zou, Honglin; Cvetković Ilić, Dragana; Zuo, Kezheng
• Is Part Of: Communications in algebra. Volume 50:Issue 8(2022)
• Page Start: 3364
• Page End: 3378
• Publication Date: 2022-08-03
• Subjects: Co-EP elements -- invertibility -- ring -- matrices; 15A09 -- 16W10 -- 16B99; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2022.2032120
• Languages: English
• ISSNs: 0092-7872

Abstract

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.