Abstract
The paper introduces the left and right versions of the large class of Drazin inverses in terms of the left and right annihilators in a ring, which are called left-Drazin and right-Drazin inverses. We characterize some basic properties of these one-sided Drazin inverses, and discuss Jacobson's lemma for them. In addition, the relation between the Drazin inverses and these two one-sided inverses is given by means of the spectrum and the operator decomposition. As an application, the left-Drazin and right-Drazin invertibilities in the Calkin algebra are investigated.
| Original language | English |
|---|---|
| Article number | 2450064 |
| Journal | Journal of Algebra and its Applications |
| Volume | 23 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 1 Mar 2024 |
Keywords
- Fredholm operators
- Jacobson's lemma
- Left-Drazin and right-Drazin inverses
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Ren, Y., & Jiang, L. (2024). Left and right-Drazin inverses in rings and operator algebras. Journal of Algebra and its Applications, 23(4), Article 2450064. https://doi.org/10.1142/S0219498824500646