Additive Results for the Generalized Drazin Inverse in a Banach Algebra

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Abstract

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.

Keywords

Generalized Drazin inverse Additive properties Banach algebras 

Mathematics Subject Classification

46H05 47A05 15A09 

Notes

Acknowledgments

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.

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Copyright information

© Malaysian Mathematical Sciences Society and Universiti Sains Malaysia 2015

Authors and Affiliations

  1. 1.Faculty of Sciences and MathematicsUniversity of NišNisSerbia

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