New additive results show an upper bound for group inverse in Banach algebra, indicating how perturbations affect its representation.
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.
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Liu et al. (2025) studied this question.
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