Perturbation for the Group Inverse in a Banach Algebra

OpenAlex İngilizce

We present new additive results for the group inverse in a Banach algebra under certain perturbations. The upper bound of ∥(a+b)#−ad∥ is thereby given. These results extend the main results presented by Liu, Qin, and Wei. We then apply them to establish the representation of the group inverse of a+b under a kind of commutative perturbation condition. Finally, some numerical examples are given to demonstrate the main results.