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Bull. Korean Math. Soc. 2014; 51(3): 765-771

Printed May 31, 2014

https://doi.org/10.4134/BKMS.2014.51.3.765

Copyright © The Korean Mathematical Society.

Group inverse and generalized Drazin inverse of block matrices in a Banach algebra

Dijana Mosi\'c

University of Ni\v s

Abstract

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Necessary and sufficient conditions for the existence of the group inverse of an anti-triangular block matrix in Banach algebras are presented. Using these results, we give the formulae for the generalized Drazin inverse of a block matrix.

Keywords: generalized Drazin inverse, reverse order law, block matrix

MSC numbers: 46H05, 47A05, 15A09

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