Cline’s formula for the generalized Drazin inverse
نویسندگان
چکیده
†Department of Mathematics, Southeast University, Nanjing 210096, China ‡College of Mathematics and Information Science, Guangxi University, Nanning 530004, China E-mail: [email protected] E-mail: [email protected] E-mail: [email protected] Abstract: It is well known that for an associative ring R, if ab is Drazin invertible then ba is Drazin invertible. In this case, (ba)D = b((ab)D)2a. This formula is so-called Cline’s formula. In this note, we generalize Cline’s formula to the case of the generalized Drazin invertibility.
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Generalized Drazin inverse of certain block matrices in Banach algebras
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