A generalization of the co-EP property

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A generalization of the co-EP property

Zou, Honglin; Cvetković Ilić, Dragana; Zuo, Kezheng

Communications in algebra, 08/2022, Volume: 50, Issue: 8

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We establish different characterizations for the invertibility of ab − ba in a ring when and 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 that are invertible independently of the choice of the scalars. In addition, we consider the co-EP-ness of idempotents and tripotents.

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Zou, Honglin | Cvetković Ilić, Dragana | Zuo, Kezheng

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