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Extended g-Drazin Inverse in a Banach Algebra

  • Dijana MosićEmail author
Article
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Abstract

We introduce and investigate a new generalized inverse as an extension of the g-Drazin inverse in a Banach algebra. This new inverse will be called an extended g-Drazin inverse. Using idempotents, we characterize this inverse and give some its representations. Also, we prove generalizations of Cline’s formula for extended g-Drazin inverse. As a consequence of our results, we present the definition and characterizations of an extended Drazin inverse.

Keywords

g-Drazin inverse Idempotent Cline’s formula Banach algebra 

Mathematics Subject Classification

46H05 46H99 15A09 

Notes

Acknowledgements

The author is grateful to the referee for careful reading of the paper.

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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2019

Authors and Affiliations

  1. 1.Faculty of Sciences and MathematicsUniversity of NišNišSerbia

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