Additive Results for the Generalized Drazin Inverse in a Banach Algebra
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Under new conditions on Banach algebra elements a and b, we derive explicit expressions for the generalized Drazin inverse of the sum \(a+b\). As an application of our results, we present new representations for the generalized Drazin inverse of a block matrix in a Banach algebra.
KeywordsGeneralized Drazin inverse Additive properties Banach algebras
Mathematics Subject Classification46H05 47A05 15A09
The author is grateful to the referee for constructive comments towards improvement of the original version of this paper. The author is supported by the Ministry of Education and Science, Republic of Serbia, Grant No. 174007.
- 10.Liu, X., Qin, X.: Representations for the generalized Drazin inverse inverse of the sum in a Banach algebra and its appication for some operator matrices. Sci. World J. 2015 (2015), Article ID 156934, p 8Google Scholar