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<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\pi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>π</mi> </math></EquationSource> </InlineEquation>-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.</p>

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

  • 期刊论文

  • 发表日期：

    2026年2月19日

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  • Kai Yan

摘要

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 \(\pi \) π -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.