Group inverse and generalized Drazin inverse of block matrices in a Banach algebra
Bull. Korean Math. Soc. 2014 Vol. 51, No. 3, 765-771
https://doi.org/10.4134/BKMS.2014.51.3.765
Published online May 31, 2014
Dijana Mosi\'c
University of Ni\v s
Abstract : 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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