Semi-B-Browder elements and Drazin invertible elements in Banach algebras

Yingying Kong; Yingying Kong

doi:10.3934/era.2026042

Electronic Research Archive

2026, Volume 34, Issue 2: 910-921. doi: 10.3934/era.2026042

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Research article

Semi-B-Browder elements and Drazin invertible elements in Banach algebras

Yingying Kong ^,

School of Mathematics and Statistics, Huanghuai University, Zhumadian 463000, China

Received: 11 November 2025 Revised: 13 January 2026 Accepted: 20 January 2026 Published: 28 January 2026

This paper studies left (right) Drazin invertible elements in a semisimple Banach algebra and provides the characterizations of the left (right) Drazin invertible elements. In addition, the paper proves that the left Drazin spectrum is compact. Finally, it is shown that being Drazin invertible is equivalent to being semi-B-Browder.
- semi-B-Browder elements,
- semi-B-Fredholm elements,
- left Drazin invertible,
- spectrum,
- Drazin invertible
Citation: Yingying Kong. Semi-B-Browder elements and Drazin invertible elements in Banach algebras[J]. Electronic Research Archive, 2026, 34(2): 910-921. doi: 10.3934/era.2026042

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Abstract

This paper studies left (right) Drazin invertible elements in a semisimple Banach algebra and provides the characterizations of the left (right) Drazin invertible elements. In addition, the paper proves that the left Drazin spectrum is compact. Finally, it is shown that being Drazin invertible is equivalent to being semi-B-Browder.

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