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arXiv · 2504.18995

On the spectral identities and fundamental properties of one-sided Drazin inverses in Banach algebras

Kai Yan
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Abstract

We establish several fundamental properties of one-sided (generalized) Drazin inverses in Banach algebras, including intertwining properties and reverse order laws. In particular, we introduce the concepts of one-sided strongly pi-regularity, which is shown to be equivalent to one-sided Drazin invertibility. By utilizing the Jacobson's lemma for one-sided regularity, we prove the Jacobson's lemma for one-sided (generalized) Drazin invertibility. These results allow us to derive the spectral identities for one-sided (generalized) Drazin invertible spectra in Banach algebras, as well as the spectral identities for Fredholm type operators acting on Banach spaces.

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Kai Yan. 2025-04-26. On the spectral identities and fundamental properties of one-sided Drazin inverses in Banach algebras. https://arxiv.org/abs/2504.18995

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