This research proposes a formula for generalized Drazin T-Riesz inverses in Banach algebras, indicating conditions for their uniqueness.
For two complex unital Banach algebras A and B and a homomorphism algebra T: A ? B having the strong Riesz property, we propose a new formula for generalized Drazin T-Riesz inverses, and we give a new Laurent expansion for the resolvent of a given generalized Drazin T-Riesz invertible element. Most importantly, necessary and sufficent conditions to have the uniqueness of generalized Drazin T-Riesz inverse are given.
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Abad et al. (2025) studied this question.
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