巴拿赫代数上伪n强Drazin逆的可加性质
Additive Property of Pseudo n-Strong Drazin Inverse of Elements in Banach Algebras
DOI: 10.12677/pm.2026.163071, PDF,   
作者: 王炜锋：浙江邮电职业技术学院继续教育学院，浙江 绍兴
关键词: 伪强Drazin逆；可加性质；巴拿赫代数；Pseudo -Strong Drazin Inverse； Additive Properties； Banach Algebra
摘要: 本文研究伪 n 强Drazin逆在巴拿赫代数上的可加性质，证明了在 a 和 b 可交换的条件下， a+b 和 1+ a pnsD b 的伪 n 强Drazin可逆性是等价的，同时我们还给出了它们伪 n 强Drazin逆之间的关系。
Abstract: This paper studies the additive properties of pseudo n -strong Drazin inverses in Banach algebras, proving that under the condition that a and b are commutative, the pseudo n -strong Drazin Invertibility of a+b and 1+ a pnsD b is equivalent. At the same time, we also provide the relationship between their pseudo n -strong Drazin inverses.
文章引用：王炜锋. 巴拿赫代数上伪n强Drazin逆的可加性质[J]. 理论数学, 2026, 16(3): 76-82. https://doi.org/10.12677/pm.2026.163071

参考文献

[1] Lam, T.Y. (1991) A First Course in Noncommutative Rings (Vol. 131). Springer. [Google Scholar] [CrossRef] 
[2] Müller, V. (2007) Spectral Theory of Linear Operators: And Spectral Systems in Banach Algebras. Birkhäuser Basel.
[3] Drazin, M.P. (1958) Pseudo-inverses in Associative Rings and Semigroups. The American Mathematical Monthly, 65, 506-514. [Google Scholar] [CrossRef] 
[4] Wang, Z. and Chen, J. (2012) Pseudo Drazin Inverses in Associative Rings and Banach Algebras. Linear Algebra and Its Applications, 437, 1332-1345. [Google Scholar] [CrossRef] 
[5] Mosić, D. (2019) The Generalized and Pseudo n-Strong Drazin Inverses in Rings. Linear and Multilinear Algebra, 69, 361-375. [Google Scholar] [CrossRef] 
[6] Hartwig, R.E., Wang, G. and Wei, Y. (2001) Some Additive Results on Drazin Inverse. Linear Algebra and Its Applications, 322, 207-217. [Google Scholar] [CrossRef] 
[7] Zhu, H. and Chen, J. (2014) Additive Property of Pseudo Drazin Inverse of Elements in Banach Algebras. Filomat, 28, 1773-1781. [Google Scholar] [CrossRef] 
[8] Hua, L. (1949) On the Automorphisms of a Sfield. Proceedings of the National Academy of Sciences of the United States of America, 35, 386-389. [Google Scholar] [CrossRef] [PubMed]
[9] Wei, Y. and Deng, C. (2011) A Note on Additive Results for the Drazin Inverse. Linear and Multilinear Algebra, 59, 1319-1329. [Google Scholar] [CrossRef] 
[10] Zhuang, G., Chen, J., Cvetković-Ilić, D.S. and Wei, Y. (2011) Additive Property of Drazin Invertibility of Elements in a Ring. Linear and Multilinear Algebra, 60, 903-910. [Google Scholar] [CrossRef] 
[11] Wang, Z. (2017) A Class of Drazin Inverses in Rings. Filomat, 31, 1781-1789. [Google Scholar] [CrossRef] 
[12] Zou, H., Mosić, D., Zuo, K. and Chen, Y. (2019) On Then-Strong Drazin Invertibility in Rings. Turkish Journal of Mathematics, 43, 2659-2679. [Google Scholar] [CrossRef] 
[13] Yan, K. and Wang, W. (2025) Additive Results for the Generalized N-Strong Drazin Inverse in Banach Algebras. Journal of Algebra and Its Applications. [Google Scholar] [CrossRef] 
[14] Cui, J., Danchev, P. and Zeng, Y (2023) Some New Results on Pseudo N-Strong Drazin Inverses in Rings. arXiv: 2312.02347.
[15] Zou, H., Chen, J., Zhu, H. and Wei, Y. (2020) Characterizations for the N-Strong Drazin Invertibility in a Ring. Journal of Algebra and Its Applications, 20, Article ID: 2150141. [Google Scholar] [CrossRef] 
[16] Zou, H. and Chen, J. (2017) On the Pseudo Drazin Inverse of the Sum of Two Elements in a Banach Algebra. Filomat, 31, 2011-2022. [Google Scholar] [CrossRef] 

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