present a new generalized version of Cline's formula and Jacobson's lemma for g-Drazin inverses in a ring.These generalized results extend many known results,e.g.,Chen and Abdolyousefi[Generalized Jacobson'...present a new generalized version of Cline's formula and Jacobson's lemma for g-Drazin inverses in a ring.These generalized results extend many known results,e.g.,Chen and Abdolyousefi[Generalized Jacobson's lemma in a Banach algebra,Comm.Algebra 49(2021)3263-3272],and Yan and Zeng[The generalized inverses of the products of two elements in a ring,Turkish J.Math.44(2020)1744-1756].展开更多
For a Banach algebra A with identity and a, b, c, d ∈ A, the relations between the extended g-Drazin inverse(resp. generalized strong Drazin inverse)of ac and that of bd are given, when bac = bdb and cac = cdb.
基金supported by the Natural Science Foundation of Zhejiang Province,China(No.LY21A010018).
文摘present a new generalized version of Cline's formula and Jacobson's lemma for g-Drazin inverses in a ring.These generalized results extend many known results,e.g.,Chen and Abdolyousefi[Generalized Jacobson's lemma in a Banach algebra,Comm.Algebra 49(2021)3263-3272],and Yan and Zeng[The generalized inverses of the products of two elements in a ring,Turkish J.Math.44(2020)1744-1756].
基金supported by the National Natural Science Foundation of China(Grant No.11901099)the Natural Science Foundation of Fujian Province(Grant No.2018J05004)。
文摘For a Banach algebra A with identity and a, b, c, d ∈ A, the relations between the extended g-Drazin inverse(resp. generalized strong Drazin inverse)of ac and that of bd are given, when bac = bdb and cac = cdb.
